FIN 3715 Test Two

A perpetuity has a PV of $20,000. If the interest rate is 6%, how much will the perpetuity pay every year?

$1200 20,000 x 0.06 = $1200

A perpetuity will pay $900 per year, starting five years after the perpetuity is purchased. What is the present value (PV) of this perpetuity on the date that it is purchased, given that the interest rate is 11%?

$5390 The first step is to calculate the PV perpetuity = $900/0.11 = $8181.82; the next step is to calculate its PV using TVM keys: input FV = $8181.82, number of years = 4, and interest rate = 11%; PV = 5389.6171

Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years. He must invest $10,000 at the start of the first year and ad additional $10,000 at the end of the first year. What is the present value of this investment if the interest rate is 3%?

3189.80

For a free-risk investment, the opportunity cost of capital will generally be more than the interest rate offered by U.S. Treasury securities with a similar term. True or False

FALSE

Joe borrows $100,000 and agrees to repay the principal, plus 7% APR interest compounded monthly, at the end of three years. Joe has taken out an amortizing loan. True or False

FALSE

The real interest rate is the rate of growth of oneʹs purchasing power due to money invested. True or False

FALSE

The term ʺopportunityʺ in opportunity cost of capital comes from the fact that any worthwhile opportunity for investment will have a cost: the risk to the capital invested. True or False

FALSE

Trial and error is the only way to compute the internal rate of return (IRR) when interest is calculated over five or more periods. True or False

FALSE

What care, if any, should be taken when cash flows occur in periodicities that are shorter than a year (e.g., quarterly or monthly cash flows)?

In the real world, cash flows can occur with any periodicity but interest rates are generally quoted in annual terms. As such, when cash flows occur at a shorter than annual time interval the interest rates have to be modified to correspond to the cash flow interval. One way to do that is to match the compounding period equal to cash flow interval.

Which of the following investments has a higher present value, assuming the same (strictly positive) interest rate applies to both investments? Investment X Year 1 = 5,000 Year 2 = 7,000 Year 3 = 9,000 Year 4 = 11,000 Investment Y Year 1 = 11,000 Year 2 = 9,000 Year 3 = 7,000 Year 4 = 5,000

Investment Y has a higher present value.

Which of the following statements regarding perpetuities is FALSE?

PV of a perpetuity = r/C

A perpetuity will pay $1000 per year, starting five years after the perpetuity is purchased. What is the future value (FV) of this perpetuity, given that the interest rate is 3%?

There is no solution to this problem. The future value of a perpetuity cannot be calculated, since there is no ending date.

Is it possible to analyze cash flows that occur in time intervals that are not exactly equal to a year?

Yes, in real world cash flows may be between any intervals. They may be shorter than a year or longer than a year. Additional care needs to be taken in both cases. For cash flows that have an interval longer than one year, one should be careful to show the years with zero cash flows. Alternately, for those with shorter than a year, one should be careful about modifying the interest rate to match the time interval.

Can we apply the growing perpetuity equation for negative growth as well?

Yes, it is perfectly in order to apply the growth perpetuity for negative growth. A negative growth gives two negatives in the denominator making it larger than a positive growth thus reducing the valuation compared to a positive growth of similar magnitude.

Which of the following yield curves would most likely predict a downturn in the economy?

test bank of 190 Answer:D

Quality adjustments to changes in the CPI most often result in reductions to the inflation rate calculated from it. True or False

TRUE

The internal rate of return (IRR) is the interest rate that sets the net present value (NPV) of the cash flows equal to zero. True or False

TRUE

The opportunity cost of capital is the best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discounted. True or False

TRUE

When you borrow money, the interest rate on the borrowed money is the price you pay to be able to convert your future loan payments into money today. True or False

TRUE

Ally wishes to leave a provision in her will that t$7000 will be paid annually in perpetuity to a local charity. How much must she provide in her will for this perpetuity if the interest rate is 6%?

$116,667 PV perpetuity = $7000/0.06 = $116,666.67

An annuity pays $10 per year for 98 years. What is the present value (PV) of this annuity given that the discount rate is 7%?

$142.67 Calculate PV annuity using TVM keys input PMT = $10, number of years = 98, and interest rate = 7%; computing PV = $142.67

A homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of $2900. After installation the solar water heater will produce a small amount of hot water every day, forever, and will require no maintenance. How much must the homeowner save on water heating costs every year if this is to be a sound investment? (The interest rate is 5% over year.)

$145 Calculate the cash flow as the perpetuity whose PV = $2900; hence, the annual heating cost = 2900 x 0.05 = $145

Joe just inherited the family business, and having no desire to run the family business, he has decided to sell it to an entrepreneur. In exchange for the family business, Joe has been offered an immediate payment of $100,000. Joe will also receive payments of $50,000 in one year, $50,000 in two years, and 75,000 in three years. The current market rate of interest for Joe is 6%. In terms of present value (PV), how much will Joe receive for selling the family business?

$254,641 PV = 100,000 + $50,000 / (1.06)^1 + 50,000 / (1.06)^2 + 75,000 / (1.06)^3 = 254,641

What is the present value (PV) of an investment that will pay $500 in one year's time, and $500 every year after that, when the interest rate is 10%?

$5000 PV Perpetuity = 500/0.1 = 5000

A business promises to pay the investor of $6000 today for a payment of $1500 in one year's time, $3000 in two years' time, and $3000 in three years' time. What is the present value of this business opportunity if the rate is 6% per year?

$603.94

An annuity is set up that will pay $1500 per year for ten years. What is the present value (PV) of this annuity given that the discount rate is 9%?

$9626 Calculate PV annuity using TVM keys: input PMT = $1500 , number of years = 10, and interest rate = 9%; PV = $9626.49 .

Define the following terms: (a) perpetuity (b) annuity (c) growing perpetuity (d) growing annuity

(a) A perpetuity is a stream of equal cash flows that occur at regular intervals and lasts forever. (b) An annuity is a stream of N equal cash flows paid at regular intervals. (c) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever. (d) A growing annuity is a stream of N growing cash flows, paid at regular intervals.

Consider the following timeline detailing a stream of cash flows: TImeline: 0 = ? 1 = 5,000 2 = 6,000 3 = 7,000 4 = 8,000 If the current market rate of interest is 10%, then the present value (PV) of this stream of cash flows is closest to: ?

A) $10,114 B) $20,227 C) $24,272 D) $32,363 Answer: B Explanation: B) PV = 5,000 / (1 + 0.1)^1 + 6,000 / (1 + 0.1)^2 + 7,000 / (1 + 0.1)^3 + 8,000 / (1 + 0.1)^4 = $20,227.44

You are thinking about investing in a mine that will produce $10,000 worth of ore in the first year. As the ore closest to the surface is removed it will become more difficult to extract the ore. Therefore, the value of the ore that you mine will decline at a rate of 7% per year forever. If the appropriate interest rate is 3%, then the value of this mining operation is closest to ________.

A) $100,000 B) $500,000 C) $250,000 D) This problem cannot be solved. Answer: A Explanation: A) PVP = C / (r - g) = $10,000 /(0.03 - -0.07 ) = $10,000 / 0.1 = $100,000

A small business repairs its store. The builders charge them $130,000 which will be paid back in monthly installments over three years at 6.80% APR. The builders will reduce this rate to 6.30% APR if they pay $2600 up front. By approximately how much will this reduce the monthly loan repayments?

A) $109 B) $218 C) $164 D) $55 Answer: A Explanation: A) The first step is to calculate the monthly payment using a present value (PV) of $130,000 monthly interest rate of 6.80 /12 = 0.566667 %, and 36 periods, which = $4002.15 ; the second step is to use that monthly payment using a monthly interest rate of 6.30 /12 = 0.525000 % and a PV of $130,000 - $2600 = $127,400 to calculate the payment = $3893.10 . The difference of the two = $4002.15 - $3893.10 = $109.05

A home buyer buys a house for $2,155,000 . She pays 20% cash, and takes a fixed-rate mortgage for ten years at 7.70% APR. If she makes semi-monthly payments, which of the following is closest to each of her payment?

A) $11,342.47 B) $10,311.34 C) $12,373.61 D) $8249.07 Answer: B Explanation: B) Calculate bimonthly payment when PV of ordinary annuity = $1,724,000 , periodicinterest=7.70/24%, andnumberofperiods=240.

Two years ago you purchased a new SUV. You financed your SUV for 60 months (with payments made at the end of the month) with a loan at 6.15% APR. Your monthly payments are $388.05 and you have just made your 24th monthly payment on your SUV. Assuming that you have made all of the first 24 payments on time, then the outstanding principal balance on your SUV loan is closest to ________.

A) $14,000 B) $12,727 C) $15,273 D) $17,818 Answer: B Explanation: B) First we need the monthly interest rate = APR / m = 0.0615 / 12 = 0.005125 or 0.5125 %. Now: I = 0.5125 FV = 0 N = 36 (remaining payments 60 - 24 = 36) PMT = 388.05 Compute PV = $12,727.23

A $50,000 new car loan is taken out with the terms 12% APR for 48 months. How much are monthly payments on this loan?

A) $1448.36 B) $1580.03 C) $1316.69 D) $1711.70 Answer: C Explanation: C) Calculate the PMT when PV of ordinary annuity = $50,000 , periodicinterest=12/12%, andnumberofperiods=48.

A $52,000 loan is taken out on a boat with the terms 3% APR for 36 months. How much are the monthly payments on this loan?

A) $1663.45 B) $1814.67 C) $1965.89 D) $1512.22 Answer: D Explanation: D) Calculate the PMT when PV of ordinary annuity = $52,000 , periodic interest = 3/12%, and number of periods = 36.

Terms in years: Rate: 1 = 1.8% 2 = 2.25% 3 = 2.30% 4 = 2.66% 5 = 3.13% The table above shows the interest rates available from investing in risk-free U.S. Treasury securities with different investment terms. What is the present value (PV) of cash flows from an investment that yields $6000 at the end of each year for the next four years?

A) $18,111 B) $27,167 C) $31,695 D) $22,639 Answer: D Explanation: D) PV of $11,000 at 1.8% for 1 year = $5893.91 ; PV of $11,000 at 2.25% for 2 years = $5710.89 ; PV of $11,000 at 2.30% for 3 years = $5604.34 ; PV of $11,000 at 2.66% for 4 years = $5401.90 ; sum of these four PVs = $22,638.99 .

You are purchasing a new home and need to borrow $260,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.80% APR for a 30-year fixed rate mortgage. The mortgage lender also tells you that if you are willing to pay two points, they can offer you a lower rate of 6.50% APR for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points, you will need to borrow an additional $5200 to cover points you are paying the lender. Assuming you pay the points and borrow from the mortgage lender at 6.50%, then your monthly mortgage payment (with payments made at the end of the month) will be closest to ________.

A) $1844 B) $1676 C) $2011 D) $2347 Answer: B Explanation: B) First we need the monthly interest rate = APR / m = 0.0650 / 12 = 0.005417 or 0.5417 %. Now: PV = 265,200 (2 points) I = 0.5417 FV = 0 N = 360 (30 years × 12 months) Compute PMT = $1676.24 .

A Xerox DocuColor photocopier costing $44,000 is paid off in 60 monthly installments at 6.90% APR. After three years the company wishes to sell the photocopier. What is the minimum price for which they can sell the copier so that they can cover the cost of the balance remaining on the loan?

A) $19,433 B) $15,546 C) $23,319 D) $27,206 Answer: A Explanation: A) The first step is to calculate the monthly payment using a present value (PV) of $44,000 monthly interest rate of 6.90 /12% = 0.575000 %, and 60 periods, which = $869.18 ; the second step is to use that monthly payment to calculate the present value (PV) of 24 months remaining payment keeping the interest rate unchanged.

Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $240,000 , or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4800 (paid at the end of each month). Your firm can borrow at 7.80% APR with quarterly compounding. The present value (PV) of the lease payments for the delivery truck is closest to ________.

A) $190,506 B) $238,132 C) $285,758 D) $333,385 Answer: B Explanation: B) First we need to calculate the monthly discount rate for the lease arrangement. EAR=(1+APR/m)m-1=(1+0.078 /4)4-1=0.08031 or8.031% Monthly rate = (1 + EAR)(1/12) - 1= (1 + 0.08031 )(1/12) - 1 = 0.006458 = 0.6458 % Now we can apply the PVA formula to calculate the PV of the lease or by calculator: I = 0.6458 N = 60 (5 years × 12 months/yr) FV = 0 PMT = $4800 Compute PV = $238,132 .

Five years ago you took out a 30-year mortgage with an APR of 6.20% for $206,000 . If you were to refinance the mortgage today for 20 years at an APR of 3.95%, how much would you save in total interest expense?

A) $200,503 B) $150,377 C) $50,126 D) $100,251 Answer: D D) Current Mortgage Payment: P/Y = 12, N = 360, I/Y = 6.20 , PV = $206,000 , Solve forPMT= 1261.69 Current Mortgage Balance: P/Y = 12, N = 300, I/Y = 6.20 , PMT = 1261.69 , Solve for PV = $192,159.69 Total of Remaining Payments on Current Mortgage = 300 × $1261.69 = $378,505.83 New Mortgage Payment: P/Y = 12, N = 240, I/Y = 3.95 , PV = $192,159.69 , Solve for PMT = $1159.39 Total Payments on New Mortgage: 240 × $1159.39 = $278,254.41 Difference in Total of Payments = $378,505.83 - $278,254.41 = $100,251`

Two years ago you purchased a new SUV. You financed your SUV for 60 months (with payments made at the end of the month) with a loan at 5.95% APR. Your monthly payments are $386.19 and you have just made your 24th monthly payment on your SUV. The amount of your original loan is closest to ________.

A) $22,000 B) $20,000 C) $24,000 D) $28,000 Answer: B Explanation: B) First we need the monthly interest rate = APR / m = 0.0595 / 12 = 0.004958 or 0.4958 %. Now: I = 0.4958 FV = 0 N = 60 PMT = $386.19 Compute PV = $20,000

A small foundry agrees to pay $220,000 two years from now to a supplier for a given amount of coking coal. The foundry plans to deposit a fixed amount in a bank account every three months, starting three months from now, so that at the end of two years the account holds $220,000 . If the account pays 12.5% APR compounded monthly, how much must be deposited every three months?

A) $24,602 B) $27,063 C) $29,523 D) $31,983 Answer: A Explanation: A) Calculate the EAR = 13.2416 %; calculate APR with quarterly compounding = 12.6307 %; calculate the payment for 8 quarters with $220,000 as future value (FV).

A truck costing $111,000 is paid off in monthly installments over four years with 8.10% APR. After three years the owner wishes to sell the truck. What is the closest amount from the following list that he needs to pay on his loan before he can sell the truck?

A) $24,956 B) $37,434 C) $31,195 D) $43,673 Answer: C Explanation: C) The first step is to calculate the monthly payment using a present value (PV) of $111,000 monthly interest rate of 8.10 /12 = 0.675000 %, and 48 periods, which = $2715.05 ; the second step is to use that monthly payment to calculate the present value (PV) of 12 months remaining payment keeping the interest rate unchanged.

You are purchasing a new home and need to borrow $380,000 from a mortgage lender. The mortgage lender quotes you a rate of 5.75% APR for a 30-year fixed rate mortgage. The mortgage lender also tells you that if you are willing to pay two points, they can offer you a lower rate of 5.45% APR for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points, you will need to borrow an additional $7600 to cover points you are paying the lender. Assuming you do not pay the points and borrow from the mortgage lender at 5.75%, then your monthly mortgage payment (with payments made at the end of the month) will be closest to ________.

A) $2439 B) $2661 C) $2218 D) $3105 Answer: C Explanation: C) First we need the monthly interest rate = APR / m = 0.0575 / 12 = 0.004792 or 0.4792 %. Now: PV = $380,000 (no points) I = 0.4792 FV = 0 N = 360 (30 years × 12 months) Compute PMT = $2217.58 .

Corey buys 10 Tufflift 4-post, 4.5-ton car hoists for his parking garage at a total cost of $432,000 . He finances this with a five-year loan at 7.80% APR with monthly payments. After he has made the first 20 payments, how much is the outstanding principal balance on his loan?

A) $244,965 B) $428,689 C) $306,206 D) $612,412 Answer: C Explanation: C) The first step is to calculate the monthly payment using a present value (PV) of $432,000 , monthly interest rate of 7.80 /12 = 0.650000 %, and 60 periods, which = $8718.11 ; the second step is to use that monthly payment to calculate the present value (PV) of 40 months keeping the interest rate unchanged, which = $306,206.10

Suppose the term structure of interest rates is shown below: Term: Rate (EAR%): 1=5.00% 2=4.80% 3=4.60% 5=4.50% 10=4.25% 20=4.15% The present value (PV) of receiving $1100 per year with certainty at the end of the next three years is closest to ________.

A) $3010 B) $2408 C) $3612 D) $4214 Answer: A Explanation: A) PV = $1100 / (1 + 0.050) + $1100 / (1 + 0.048)2 + $1100 / (1 + 0.046)3 = 3010.33

Liam had an extension built onto his home. He financed it for 48 months with a loan at 5.00% APR. His monthly payments were $770 . How much was the loan amount for this extension?

A) $33,436 B) $40,123 C) $46,810 D) $53,497 Answer: A Explanation: A) Calculate the PV annuity of $770 for 48 months at 5.00 /12 = 0.416667 %, which = $33,436

What is the present value (PV) of an investment that pays $100,000 every year for four years if the interest rate is 5% APR, compounded quarterly?

A) $353,818 B) $389,200 C) $424,581 D) $459,963 Answer A Explanation: Diff: 2 Var: 35 Skill: Analytical AACSB Objective: Analytic Skills Author: DS Question Status: Previous Edition A) Calculate EAR = 5.0945 %; Calculate PV Annuity = $353,818

You are considering purchasing a new automobile with the upfront cost of $25,000 or leasing it from the dealer for a period of 60 months. The dealer offers you 4.00% APR financing for 60 months (with payments made at the end of the month). Assuming you finance the entire $25,000 through the dealer, your monthly payments will be closest to ________.

A) $368 B) $460 C) $552 D) $645 Answer: B Explanation: B) First we need the monthly interest rate = APR / m = 0.0400 / 12 = 0.003333 or 0.3333 %.

An investment pays you 30,000 at the end of this year, and 10,000 at the end of each of the following years. What is the present value (PV) of this investment, given that the interest rate is 5% per year?

A) $39,614 B) $63,382 C) $79,228 D) $95,074 Answer: C

You are considering purchasing a new automobile with the upfront cost of $26,000 or leasing it from the dealer for a period of 48 months. The dealer offers you 2.80% APR financing for 48 months (with payments made at the end of the month). Assuming you finance the entire $26,000 through the dealer, your monthly payments will be closest to ________.

A) $459 B) $688 C) $573 D) $802 Answer: C Explanation: C First we need the monthly interest rate = APR / m = 0.0280 / 12 = 0.002333 or 0.002333 %. Now: PV = $26,000 I = 0.2333 FV = 0 N = 48 Compute PMT = $573.20 .

You are interested in purchasing a new automobile that costs $33,000 . The dealership offers you a special financing rate of 9% APR (0.75% per month) for 60 months. Assuming that you do not make a down payment on the auto and you take the dealerʹs financing deal, then your monthly car payments would be closest to ________.

A) $548 B) $685 C) $959 D) $1096 Answer: B Explanation: B) PV = 33,000 I = 0.75 N = 60 FV = 0 Compute payment = $685.03 .

An investor buys a property for $608,000 with a 25-year mortgage and monthly payments at 8.10% APR. After 18 months the investor resells the property for $667,525 . How much cash will the investor have from the sale, once the mortgage is paid off?

A) $57,216 B) $100,129 C) $71,521 D) $143,041 Answer: C Explanation: C) The first step is to calculate the monthly payment using a present value (PV) of $608,000 , monthly interest rate of 8.10 /12 = 0.675000 %, and 300 periods, which = $4732.9906 ; the second step is to use that monthly payment to calculate the present value (PV) of 282 months keeping the interest rate unchanged which = $596,004.59 ; finally calculate the difference between $667,525 - $596,004.59 = $71,520.55 .

A homeowner has five years of monthly payments of $1400 before she has paid off her house. If the interest rate is 6% APR, what is the remaining balance on her loan?

A) $57,933 B) $86,899 C) $72,416 D) $101,382 Answer: C Explanation: C) Calculate PV of the ordinary annuity of $1400 paid per month at a periodic interest rate of 6 /12 = 0.500000 % over 60 months = $72,416 .

A bank lends some money to a business. The business will pay the bank a single payment of $176,000 in ten yearsʹ time. How much greater is the present value (PV) of this payment if the interest rate is 9% rather than 8%?

A) $7178 B) $5742 C) $8613 D) $10,049 Answer: A Explanation: A) PV of $180,000 at 8% for 10 years = $81,522.05 PV of $180,000 at 9% for 10 years = $74,344.30 ; difference = $7177.75

The table above shows the interest rates available from investing in risk-free U.S. Treasury securities with different investment terms. If an investment offers a risk-free cash flow of $100,000 in two yearsʹ time, what is the present value (PV) of that cash flow? Terms in Years: Rate: 2 = 2.25% 5 = 3.125% 10=3.5% 30=4.375%

A) $76,518 B) $114,777 C) $133,906 D) $95,647 Answer: D Explanation: D) Using FV = $100,000 , find the present value (PV) at 2.25 % for 2 years.

Suppose the term structure of interest rates is shown below: Term: Rate (EAR%): 1=5.00% 2=4.80% 3=4.60% 5=4.50% 10=4.25% 20=4.15% The net present value (NPV) of an investment that costs $4320 and pays $1600 certain at the end of one, three, and five years is closest to ________.

A) $91.37 B) $137.05 C) $114.21 D) -$114.21 Answer: D Explanation: D) NPV = -4320 + 1600 / (1.05)1 +1600 / (1.046)3 + 1600 / (1.045)5 = -$114.21

A lottery winner will receive $6 million at the end of each of the next twelve years. What is the future value (FV) of the winnings at the time of her final payment, given that the interest rate is 8.6% per year?

A) $94.40 million B) $118.00 million C) $165.20 million D) $188.80 million Answer: B Explanation: B) Calculate the FV with PMT = $6 million, interest = 8.6%, and N = 12, which gives FV = $118.00 million.

In 2009, U.S. Treasury yielded 0.1%, while inflation was 2.7%. What was the real rate in 2009?

A) -2.6% B) 2.6% C) -2.8% D) 2.8% Answer: A Explanation: A) 0.1% - 2.7% = -2.6%

A construction company takes a loan of $1,531,000 to cover the cost of a new grader. If the interest rate is 6.75% APR, and payments are made monthly for five years, what percentage of the outstanding principal does the company pay in interest each month?

A) 0.56% B) 5.63% C) 0.51% D) 0.61% E) 0.66% Answer: A Explanation: A) The percentage of outstanding principal paid is the monthly periodic interest rate = 6.75/12 = 0.56%.

In 2007, interest rates were about 4.5% and inflation was about 2.8%. What was the real interest rate in 2007?

A) 1.58% B) 1.61% C) 1.62% D) 1.65% Answer: D D) 1.045 / 1.028 = 1.0165; real rate = 1.65%

A 10% APR with quarterly compounding is equivalent to an EAR of ________.

A) 10.00% B) 10.47% C) 10.38% D) 9.81% Answer: C Explanation: C) EAR=(1+0.10/4)4-1=10.38%

If the current inflation rate is 2.0%, then the nominal rate necessary for you to earn a(n) 7.3% real interest rate on your investment is closest to ________.

A) 11.3% B) 9.4% C) 13.2% D) 15.1% Answer: B Explanation: B) nominal = (1 + inflation)(1 + real) - 1 = (1 + 0.073)(1 + 0.02) - 1 = 0.0945or 9.4%

Michael has a credit card debt of $75,000 that has a 12% APR, compounded monthly. The minimum monthly payment only requires him to pay the interest on his debt. He receives an offer for a credit card with an APR of 4% compounded monthly. If he rolls over his debt onto this card and makes the same monthly payment as before, how long will it take him to pay off his credit card debt?

A) 112 months B) 113 months C) 120 months D) 122 months Answer: D Explanation: D) The first step is to calculate the minimum monthly payment using the debt balance of $75,000 and 12% APR compounded monthly, which = $75,000 × 12% / 12 = $750 . The second step is to use the same $750 as payment, and using a discount rate of 4%/12, calculate the number of months required to pay off the present value (PV) of $75,000 , which = 122 months.

Suppose the term structure of interest rates is shown below: Term: Rate (EAR%): 1=5.00% 2=4.80% 3=4.60% 5=4.50% 10=4.25% 20=4.15% Consider an investment that pays $1900 certain at the end of each of the next four years. If the investment costs $6650 and has a net present value (NPV) of $142.31 , then the four year risk-free interest rate is closest to ________.

A) 4.01% B) 3.51% C) 5.01% D) 4.51% Answer: D Explanation: D) NPV = 142.31 = -6650 + 1900 / (1.05)1 + 1900 / (1.048)2 + 1900 / (1.046)3 +1900 / (1 + x)4 6650 + 142.31 - 1900 / (1.05)1 + 1900 / (1.048)2 + 1900 / (1.046)3 = 1900 / (1 + x)4 X=0.0451 or4.51%

A homeowner has a $227,000 home with a 20-year mortgage, paid monthly at 6.60% APR. After five years he receives $50,000 as an inheritance. If he pays this $50,000 toward his mortgage along with his regular payment, by approximately how many years will it reduce the amount of time it takes him to pay off his mortgage?

A) 5.5 years B) 8.6 years C) 10.2 years D) 12.8 years Answer: A Explanation: A) The first step is to calculate the monthly payment using a present value (PV) of $227,000 , monthly interest rate of 6.60 /12 = 0.55 %, and 240 periods, which = $1705.842 ; the second step is to use that monthly payment to calculate the balance at the end of five years, which = $194,594.353 ; next step is to reduce this balance by $50,000 to the new outstanding balance of $144,594.353 ; now calculate the number of months required to pay off this balance, which = 114.45 ; the last step is to calculate the difference between 180 - 114.45 = 65.55 , when divided by 12 gives 5.5 years.

Joseph buys a Hummer for $59,000 , financing it with a five-year 7.60% APR loan paid monthly. He decides to pay an extra $50 per month in addition to his monthly payments. Approximately how long will he take to pay off the loan under these conditions?

A) 59.57 months B) 57.07 months C) 54.57 months D) 60.57 months Answer: B Explanation: B) The first step is to calculate the monthly payment using a present value (PV) of $59,000 , monthly interest rate of 7.60 /12 = 0.633333 %, and 60 periods, which = $1185.04 ; the second step is to add $50 to this monthly payment giving the new monthly payment of $1235.04 ; the last step is to calculate the time required to pay off the loan = 57.0740 months.

A house costs $148,000 . It is to be paid off in exactly ten years, with monthly payments of $1737.54 . What is the APR of this loan?

A) 6.25% B) 5.25% C) 7.25% D) 8.25% Answer: C Explanation: C) Calculate the periodic interest rate when PV of ordinary annuity = $148,000 , number of months = 120, and monthly payments = $1737.54 ; the periodic interest rate = 0.60 %, which multiplied by 12 gives an APR = 7.25 %.

What is the real interest rate given a nominal rate of 8.9% and an inflation rate of 1.9%?

A) 6.9% B) 8.2% C) 9.6% D) 11.0% Answer: A Explanation: A) (0.089 ) / (1+ 0.019 ) - 1 = 0.06869 ;real rate = 6.869 %

Elinore is asked to invest $5100 in a friendʹs business with the promise that the friend will repay $5610 in one year. Elinore finds her best alternative to this investment, with similar risk, is one that will pay her $5508 in one year. U.S. securities of similar term offer a rate of return of 7%. What is the opportunity cost of capital in this case?

A) 7% B) 8% C) 9% D) 10% Answer: B Explanation: B) $5508 - $5100 = $408 ; $408 / $5100 = 0.08 or 8%

Ursula wants to buy a $19,000 used car. She has savings of $2,000 plus an $800 trade-in. She wants her monthly payments to be about $282 . Which of the following loans offers monthly payments closest to $282?

A) 7.8% APR for 36 months B) 7.8% APR for 48 months C) 7.8% APR for 60 months D) 7.8% APR for 72 months Answer: D Explanation: D) Calculate N when PV of ordinary annuity = $19,000 - $2,000 - $800 = $16,200 , periodic interest=7.8/12%, and monthly payments=$282.

A pottery factory purchases a continuous belt conveyor kiln for $68,000 . A 6.3% APR loan with monthly payments is taken out to purchase the kiln. If the monthly payments are $765.22 , over what term is this loan being paid?

A) 8 years B) 9 years C) 10 years D) 11 years Answer: C Explanation: C) Calculate N when PV of ordinary annuity = $68,000 , periodicinterest=6.3/12%, andmonthlypayments=$765.22. N = 156 periods; years = 13 years.

If the current inflation rate is 3.6% and you have an investment opportunity that pays 10.9%, then the real rate of interest on your investment is closest to ________.

A) 8.5% B) 9.9% C) 11.3% D) 7.0% Answer: D Explanation: D) (1 + nominal rate) = (1 + inflation rate)(1 + real rate) real interest rate = 1 + nominal rate/1 + inflation rate - 1 = 0.070463 or 7.05 %

Historically, why were high inflation rates associated with high nominal interest rates?

A) Individuals will spend more when they expect their investments to increase in value. B) Growth in investment and savings is encouraged when consumers are judged to be overspending. C) High inflation leads to a decrease in purchasing power and thus increases the attractiveness of investment over consumption in the short term. D) The real interest rate needs to be high enough so that individuals can expect their savings to have greater purchasing power in the future than in the present. Answer: D

When the costs of an investment come before that investmentʹs benefits, what will be the effect of a rise in interest rates on the attractiveness of that investment to potential investors?

A) It will make it more attractive, since it will increase the investmentʹs net present value (NPV). B) It will make it more attractive, since it will decrease the investmentʹs net present value (NPV). C) It will make it less attractive, since it will increase the investmentʹs net present value (NPV). D) It will make it less attractive, since it will decrease the investmentʹs net present value (NPV). Answer: D

Emma runs a small factory that needs a vacuum oven for brazing small fittings. She can purchase the model she needs for $180,000 up front, or she can lease it for five years for $4,200 per month. She can borrow at 7% APR, compounded monthly. Assuming that the oven will be used for five years, should she purchase the oven or should she lease it?

A) Lease, since the present value (PV) of the lease is $12,224 less than the cost of the oven. B) Lease, since the present value (PV) of the lease is $8,642 less than the cost of the oven. C) Lease, since the present value (PV) of the lease is $2,212 less than the cost of the oven. D) Buy, since the present value (PV) of the lease is $32,108 more than the cost of the oven. Answer: D Explanation: D) Calculate PV lease payments = $212,108; subtract $180,000 to get $32,108.

In an effort to maintain price stability, it is expected that the European Central Bank will raise interest rates in the future. Which of the following is the most likely effect of such an action on short-term and long-term interest rates in Europe?

A) Long-term interest rates will tend to be higher than short-term interest rates. B) Long-term interest rates will be about the same as short-term interest rates. C) Both long- and short-term interest rates would be expected to fall sharply. D) No relative change in short and long term interest rates could be predicted. Answer: A

Why, in general, do investment opportunities offer a rate greater than that offered by U.S. Treasury securities for the same horizon?

A) Most investment opportunities bear far greater risk than those offered by U.S. Treasury securities. B) The return from U.S. Treasury securities generally attracts less tax than the returns from other investments. C) The opportunity cost of capital for a given horizon is generally based on U.S. Treasury securities with that same horizon. D) U.S. Treasury securities are generally considered to be the best alternative to most investments. Answer: A

Which of the following is/are TRUE? I. The EAR can never exceed the APR. II. The APR can never exceed the EAR. III. The APR and EAR can never be equal.

A) Only I is true. B) Only II is true. C) Only II & III are true. D) Only I & III are true. Answer: B

Given the above term structure of interest rates, which of the following is most likely in the future? Option I. = Interest rates will fall. Option II. = Economic growth will slow. Option III. = Long-term rates will rise relative to short term rates.

A) Option I only B) Option II only C) Option III only D) Options I and II Answer: A

Which of the following situations would result in lowering of interest rates by the banking authority of a country?

A) The economy is slowing down. B) Inflation is rising rapidly. C) The level of investment is quite high. D) The rate of savings is quite low. Answer: A

Five years ago you took out a 30-year mortgage with an APR of 6.5% for $200,000. If you were to refinance the mortgage today for 20 years at an APR of 4.25%, how much would your monthly payment change by?

A) The monthly payment will increase by $104.79. B) The monthly payment will decrease by $104.79 C) The monthly payment will increase by $343.12. D) The monthly payment will decrease by $343.12. Answer: B Current Mortgage Payment: P/Y = 12, N = 360, I/Y = 6.5, PV = $200,000, Solve for PMT = $1,264.14 Current Mortgage Balance: P/Y = 12, N = 300, I/Y = 6.5, PMT = $1,264.14, Solve for PV = $187,221.9 New Mortgage Payment: P/Y = 12, N = 240, I/Y = 4.25, PV = $187,222.54, Solve for PMT = $1,159.35 Current Payment - New Payment = $1,159.35- $1,264.14 = -$104.79

Assume your current mortgage payment is $900 per month. If you begin to pay $1,000 per month (with the extra $100 per month going to principal), which of the following will be TRUE?

A) The mortgage balance will decrease faster with $1,000 monthly payment compared to $900 monthly payments. B) The total amount paid (principal and interest) will increase with $1,000 monthly payment compared to $900 monthly payments. C) The total interest expense will increase with $1,000 monthly payment compared to $900 monthly payments. D) The total principal paid will decrease with $1,000 monthly payment compared to $900 monthly payments. Answer: A

Which of the following would be LEAST likely to lower the interest rate that a bank offers a borrower?

A) The number of borrowers seeking funds is low. B) The expected inflation rate is expected to be low. C) The borrower is judged to have a low degree of risk. D) The loan will be for a long period of time. Answer: D

Given that the inflation rate in 2006 was about 3.24%, while a short-term municipal bond offered a rate of 2.9%, which of the following statements is correct?

A) The purchasing power of investors in these bonds grew over the course of the year. B) The real interest rate for investors in these bonds was greater than the rate of inflation. C) Investors in these bonds were able to buy less at the end of the year than they could have purchased at the start of the year. D) The nominal interest rate offered by these bonds gave the true increase in purchasing power that resulted from investing in these bonds. Answer: C

Which of the following reasons for considering long-term loans inherently more risky than short-term loans is most accurate?

A) There is a greater chance that inflation may fall in a longer time-frame. B) The penalties for closing out a long term loan early make them unattractive to many investors. C) Long-term loans typically have ongoing costs that accumulate over the life of the loan. D) The loan values are very sensitive to changes in market interest rates. Answer: D

When computing a present value, which of the following is TRUE? A) You should adjust the discount rate to match the interval between cash flows. B) You should adjust the future value to match the present value. C) You should adjust the time period to match the present value. D) You should adjust the cash flows to match the time period of the discount rate.

A) You should adjust the discount rate to match the interval between cash flows.

A(n) 12% APR with monthly compounding is closest to ________.

A) an EAR of 10.14 % B) an EAR of 15.22 % C) an EAR of 12.68 % D) an EAR of 25.36 % Answer: C

The yield curve is typically ________.

A) downward sloping B) upward sloping C) flat D) inverted Answer: B

Which of the following computes the growth in purchasing power?

A) growth of money + growth of prices B) (1 + real rate) / (1 + nominal rate) C) (1 + inflation rate) / (1 + nominal rate) D) growth of money / growth of prices Answer: D

Suppose the term structure of interest rates is shown below: Term: Rate (EAR%): 1 year = 5.00% 2 years = 4.80% 3 years = 4.60% 5 years = 4.50% 10 years = 4.35% 20 years = 4.15% What is the shape of the yield curve and what expectations are investors likely to have about future interest rates?

A) inverted; higher B) normal; higher C) inverted; lower D) normal; lower Answer: C

Everything else remaining same, under what situation will APR and EAR be equal?

An APR will equal EAR only with annual compounding assuming everything else remains same.

What, typically, is used to calculate the opportunity cost of capital on a risk-free investment?

A) the best expected return offered in any investment available in the market B) the interest rate on U.S. Treasury securities with the same term C) the interest rate of any investments alternatives that are available D) the best rate of return offered by U.S. Treasury securities Answer: B

Which of the following best describes the annual percentage rate?

A) the quoted interest rate which, considered with the compounding period, gives the effective interest rate B) the effective annual rate, after compounding is taken into account C) the discount rate, when compounded more than once a year or less than once a year D) the discount rate, when effective annual rate is divided by the number of times it is compounded in a year Answer: A

Inflation is calculated as the rate of change in the _______.

A) unemployment rate B) Gross Domestic Product C) Consumer Price Index D) risk-free rate Answer: C

A bank offers an account with an APR of 5.8% and an EAR of 5.88%. How does the bank compound interest for this account?

A) weekly compounding B) monthly compounding C) semiannual compounding D) annual compounding Answer: C Explanation: C) Using an APR = 5.8%, calculate the EAR for the compounding periods given in each choice: A = 5.97%; B = 5.96%; C = 5.88%; D = 5.8%.

In which of the following situations would it not be appropriate to use the following formula: PV = C0 + C1/(1 + r) + C2/(1 + r)^2 + . . . . + Cn/(1 + r)^n when determining the present value (PV) of a cash flow stream?

A) when yield curves are flat B) when short-term and long-term interest rates vary widely C) when the inflation rate is high D) when the discount rate is high Answer: B

How do we handle a situation when both compounding period and cash flow interval are given to us but both are less than a year and not equal to each other?

Additional care should be taken when the compounding period is given to us and it does not equal the cash flow interval. This requires some additional steps in computing the applicable interest rate. The compounding interval has to match the cash flow interval to enable transformation to present value (PV) or future value (FV). In most cases, it should be possible to achieve this by calculating the effective annual rate from the given compounding interval and subsequently calculating the annual percentage rate and periodic interest rate for the cash flow interval.

Which of the following is true about perpetuities?

All else equal, the present value of a perpetuity is higher when the periodic cash flow is higher. All else equal, the present value of a perpetuity is higher when the interest rate is lower. If two perpetuities have the same present value and the same interest rate, they must have the same cash flows. All of the above are true statements.

You are in the process of purchasing a new automobile that will cost you $25,000. The dealership is offering you either a $1,000 rebate (applied toward the purchase price) or 3.9% financing for 60 months (with payments made at the end of the month). You have been pre-approved for an auto loan through your local credit union at an interest rate of 7.5% for 60 months. Should you take the $1,000 rebate and finance through your credit union or forgo the rebate and finance through the dealership at the lower 3.9% APR?

Answer: Financing through credit union: First we need the monthly interest rate = APR / m = 0.075 / 12 = 0.00625 or 0.625%. Now: PV=$24,000 (25,000 - 1,000 rebate) I = 0.625 FV = 0 N = 60 Compute PMT = $480.91. Financing through dealership: First we need the monthly interest rate = APR / m = 0.039 / 12 = 0.00325 or 0.325%. Now: PV = $25,000 (no rebate) I = 0.325 FV = 0 N = 60 Compute PMT = $459.29 Since 459.29 < 480.91, go with the dealership financing and forgo the rebate.

What is the net present value (NPV) of an investment that costs $2,500 and pays $1,000 at the end of one, three, and five years?

Answer: NPV = -$2,500 + $1,000 / (1.05)1 + $1,000 / (1.046)3 + $1,000 / (1.045)5 = $128.62

Which of the following statements regarding growing perpetuities is FALSE? A) We assume that r < g for a growing perpetuity. B) PV of a growing perpetuity = C/ r - g C) To find the value of a growing perpetuity one cash flow at a time would take forever. D) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.

Answer: A We assume that r < g for a growing perpetuity.

Which of the following statements is FALSE? A) The actual return kept by an investor will depend on how the interest is taxed. B) The equivalent after-tax interest rate is r(1 - τ). C) The highest interest rate for a given horizon is the rate paid on U.S. Treasury securities. D) It is important to use a discount rate that matches both the horizon and the risk of the cash flows.

Answer: C

Which of the following statements is FALSE? A) The interest rates that banks offer on investments or charge on loans depend on the horizon of the investment or loan. B) The Federal Reserve determines very short-term interest rates through its influence on the federal funds rate. C) The interest rates that are quoted by banks and other financial institutions are nominal interest rates. D) Fundamentally, interest rates are determined by the Federal Reserve.

Answer: D

Which of the following statements is FALSE? A) The opportunity cost of capital is the best available expected return offered in the market on an investment of comparable risk and term of the cash flows being discounted. B) Interest rates we observe in the market will vary based on quoting conventions, the term of investment, and risk. C) The opportunity cost of capital is the return the investor forgoes when the investor takes on a new investment. D) For a risk-free project, the opportunity cost of capital will typically be greater than the interest rate of U.S. Treasury securities with a similar term.

Answer: D

An annuity pays $47 per year for 22 years. What is the future value (FV) of this annuity at the end of those 22 years, given that the discount rate is 8%?

D) $2606.47 D) Using TVM keys input PMT = $47, number of years = 22, and interest rate = 8%; computing FV = $2606.47 .

You are purchasing a new home and need to borrow $325,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.5% APR for a 30-year fixed rate mortgage (with payments made at the end of each month). The mortgage lender also tells you that if you are willing to pay one point, they can offer you a lower rate of 6.25% APR for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points, you will need to borrow an additional $3,250 to cover points you are paying the lender. Assuming that you do not intend to prepay your mortgage (pay off your mortgage early), are you better off paying the one point and borrowing at 6.25% APR or just taking out the loan at 6.5% without any points?

Answer: Pay the points! Points (6.25% APR) First we need the monthly interest rate = APR / m = 0.0625 / 12 = 0.00520833 or 0.5208%. Now: PV = $328,250 ($325,000 + 1 point) I = 0.5208 FV = 0 N = 360 (30 years × 12 months) Compute PMT = $2,021.01 No Points (6.5% APR) First we need the monthly interest rate = APR / m = 0.065 / 12 = 0.005417 or 0.5417%. Now: PV = $325,000 (no points) I = 0.5417 FV = 0 N = 360 (30 years × 12 months) Compute PMT = $2,054.22 Since $2,021.01 < $2,054.22, pay the points!

Can the nominal interest rate ever be negative? Can the real interest rate ever be negative? Explain.

Answer: The nominal interest rate can never be negative since by just holding your money you are earning a 0% return (no negative) on your money. The real rate, however, can be negative anytime that the inflation rate exceeds the nominal rate.

Suppose the term structure of interest rates is shown below: Term: Rate (EAR%): 1=5.00% 2=4.80% 3=4.60% 5=4.50% 10=4.25% 20=4.15% After examining the yield curve, what predictions do you have about interest rates in the future? About future economic growth and the overall state of the economy?

Answer: This is an inverted yield curve, which implies that interest rates should be falling in the future. An inverted yield curve is often interpreted as a negative forecast for economic growth. Since each of the last six recessions in the United States were preceded by a period with an inverted yield curve it could be a leading indicator of a future recession.

How do we decide on opportunity cost when we have several opportunities that need to be foregone?

Answer: We rank all the foregone opportunities, and opportunity cost is the second best opportunity that we forego. Thus we select the best opportunity and rank all the alternative opportunities and use the cost of the second best opportunity as opportunity cost.

If the current rate of interest is 7%, then the future value (FV) of an investment that pays $1200 per year and lasts 18 years is closest to ________.

B) $40,799 Explanation: B) N = 18 I=7 PMT = $1200 PV = 0 Compute FV = $40,799

Since your first birthday, your grandparents have been depositing $100 into a savings account every month. The account pays 9% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ________.

B) $53,635 N = 216 PMT = $100 I = 9/12 PV = 0 Compute FV = $53,635.167

Which of the following statements regarding annuities is FALSE? A)PV of an annuity=C× 1 1- 1 r (1 + r)N B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. C) An annuity is a stream of N equal cash flows paid at regular intervals. D) Most car loans, mortgages, and some bonds are annuities.

B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. Explanation: A perpetuity never ends.

If the current rate of interest is 8%, then the present value (PV) of an investment that pays $1200 per year and lasts 24 years is closest to ________.

C) $12,635 N = 24 I=8 PMT = $1200 FV = 0 Compute PV = $12,635 .

You are saving money to buy a car. If you save $310 per month starting one month from now at an interest rate of 6%, how much will you be able to spend on the car after saving for 4 years?

C) $16,770.33 Explanation: C) N = 48 I = 6/12 PMT = $310 PV = 0 Compute FV = $16,770.33

When there are large numbers of people looking to save their money and there is little demand for loans, one would expect interest rates to be high. True or False

FALSE

You are borrowing money to buy a car. If you can make payments of $320 per month starting one month from now at an interest rate of 12%, how much will you be able to borrow for the car today if you finance the amount over 4 years?

D) $12,151.67 N = 48 I = 12 /12 PMT = $320 FV = 0 PV = $12,151.67

An annuity pays $13 per year for 53 years. What is the future value (FV) of this annuity at the end of that 53 years given that the discount rate is 9%?

D) $13,764.85 Using TVM keys input PMT = $13, number of years = 53, and interest rate = 9%; computing PV = $13,764.85 .

Cash flows from an annuity occur every year in the future.

False

The table above shows the rate of return (APR) for four investment alternatives. Which offers the highest EAR? Investment: Rate of Return: Compounding: A, B, C, D 6% 5.9% 5.8% 5.7% Yearly Semiannually Monthly Weekly

Investment A Explanation: A) Calculate the EAR for each; A = 6.0%; B = 5.99%; C = 5.96%; D = 5.86%.

A growing perpetuity, where the rate of growth is greater than the discount rate, will have an infinitely large present value (PV). True or False.

TRUE

Market forces determine interest rates based ultimately on the willingness of individuals, banks, and firms to borrow, save, and lend. True or False

TRUE

What is the general relationship between the absolute values of APR and EAR for an investment?

The APR of a project will either equal its EAR or be smaller than EAR. The APR will equal EAR with annual compounding for all other compounding intervals the APR will be smaller than EAR.

How are interest and return of principal handled in an amortizing loan payment?

The amount of periodic payments, generally monthly, for most amortizing loans is held constant such that a part goes toward paying interest on the outstanding balance and the rest toward return of principal. Thus this ratio keeps changing over the life of the loan. Initially, when the principal is highest, a major part of the loan goes toward paying interest and a smaller part toward returning the principal. However, as the loan progresses the interest component of the payment increases and the principal component decreases till the loan is fully paid off.

What is the implied assumption about interest rates when using the built-in functions of a financial calculator to calculate the present value (PV) of an annuity?

The built-in functions for present value of ordinary annuity in a financial calculator assume that interest rates are the same for every maturity on the yield curve.

What is the implied assumption about interest rates when the equation to calculate the present value (PV) of perpetuity is used?

The equation for computation of present value of perpetuity assumes that the interest rates are the same for every maturity on the yield curve.

Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their childʹs college education. Currently, college tuition, books, fees, and other costs average $12,500 per year. On average, tuition and other costs have historically increased at a rate of 4% per year. Assuming that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest, then what is the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education?

This is a two-step problem. Step 1. Determine the cost of the first year of college. Step 2. Figure out the value for four years of college. $97,110.01

The present value (PV) of a stream of cash flows is just the sum of the present values of each individual cash flow.

True

Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $4000 in the first year, and will grow by 7% per year, forever. If the interest rate is 9%, how much must Martin provide to fund this bequest?

A) $100,000.00 B) $160,000.00 C) $200,000.00 D) $240,000.00 Answer: C Explanation: C) PV growth perpetuity = $4000 / (0.09 - 0.07) = $200,000.00

Consider the following timeline detailing a stream of cash flows: 0=1,000 1=2,000 2=3,000 3=4,000 4=? If the current market rate of interest is 8%, then the future value (FV) of this steam of cash flows is closest to: ?

A) $11,699 B) $5850 C) $14,039 D) $18,718 Answer: A Explanation: A) $11,699 FV = 1,000(1 + 0.08)4 + 2,000(1 + 0.08)3 + 3,000(1 + 0.08)2 + 4,000(1 + 0.08)1 = $11,699

Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their childʹs college education. Currently, college tuition, books, fees, and other costs average $12,000 per year. On average, tuition and other costs have historically increased at a rate of 5% per year. Assuming that college costs continue to increase an average of 5% per year and that all her college savings are invested in an account paying 8% interest, then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to ________.

A) $110,793 B) $55,397 C) $77,555 D) $132,952 Answer: A Explanation: A) This is a two-step problem.

You are offered an investment opportunity that costs you $28,000, has a net present value (NPV) of $2278, lasts for three years, has interest rate of 10%, and produces the following cash flows: The missing cash flow from year 2 is closest to ________

A) $12,500 B) $12,000 C) $13,000 D) $10,000 Answer: B NPV = PV benefits - PV of costs $2,278 = $10,000 / (1.10)1 + X / (1.10)2 + $15,000 / (1.10)3 - $28,000 $30,278 = $10,000 / (1.10)1 + X / (1.10)2 + $15,000 / (1.10)3 $30,278 = $9,091 + X / (1.10)2 + $11,270 $9,917 = X / (1.10)2 X = 11,999.57

Clarissa wants to fund a growing perpetuity that will pay $10,000 per year to a local museum, starting next year. She wants the annual amount paid to the museum to grow by 5% per year. Given that the interest rate is 9%, how much does she need to fund this perpetuity?

A) $125,000.00 B) $200,000.00 C) $300,000.00 D) $250,000.00 Answer: D Explanation: D) PV growth perpetuity = $10,000 / (0.09 - 0.05) = $250,000.00

A bank is negotiating a loan. The loan can either be paid off as a lump sum of $80,000 at the end of four years, or as equal annual payments at the end of each of the next four years. If the interest rate on the loan is 6%, what annual payments should be made so that both forms of payment are equivalent?

A) $14,630 B) $18,287 C) $25,602 D) $29,259 Answer: B Explanation: B) Calculate PMT with FV = $80,000 , interest = 6% and N = 4, which gives PMT = $18,287.32 .

Suppose you invest $1000 into a mutual fund that is expected to earn a rate of return of 11%. The amount of money will you have in ten years is closest to which of the following? The amount you will have in 50 years is closest to which of the following?

A) $1420 ; $110,739 B) $2271 ; $166,109 C) $2839 ; $184,565 D) $3123 ; $221,478 Answer: C Explanation: C) FV = 1000 (1 + 0.11 )10 = $2839 ; FV = 1000 (1 + 0.11 )50 = $184,565

A bank offers a home buyer a 20-year loan at 8% per year. If the home buyer borrows $130,000 from the bank, how much must be repaid every year?

A) $15,888.95 B) $18,537.11 C) $21,185.26 D) $13,240.79 Answer: D Explanation: D) Calculate PMT using TVM keys: input PV = 130,000 , N = 20, and interest rate = 8%; PMT = $13,240.787 .

If 8,000 is invested in a certain business at the start of the year, the investor will receive 2,400 at the end of each of the next four years. What is the present value of this business opportunity if the interest rate is 6% per year?

A) $158.13 B) $316.25 C) $379.50 D) $506.00 Answer: B Explanation: B) CalculatetheNPVusingCFkeys:inputCF0=-$8000,CF1=$2400,andF1=4 using interest = 6%, which gives NPV = $316.25

Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $5000 per year. If he can get a four-year loan with an interest rate of 7.9%, what is the maximum price he can pay for the car?

A) $16,598 B) $19,918 C) $23,237 D) $26,557 Answer: A Explanation: A) Calculate PV using TVM keys: input PMT = $5000 , N= 4, and interest rate = 7.9%; PV = $16,597.5634 .

Consider the following timeline detailing a stream of flows: 0=100 1=200 2 = 300 3=400 4=500 5=? If the current market rate of interest is 6%, then the future value (FV) of this steam of cash flows is closest to: ?

A) $1723 B) $1,500 C) $2068 D) $2757 Answer: A Explanation: A) FV = 100(1 + 0.06)5 + 200(1 + 0.06)4 + 300(1 + 0.06)3 + 400(1 + 0.06)2 + 500(1 + 0.06)1 = $1723

Howard is saving for a holiday. He deposits a fixed amount every month in a bank account with an EAR of 14.7%. If this account pays interest every month then how much should he save from each monthly paycheck in order to have $14,000 in the account in four yearsʹ time?

A) $176 B) $308 C) $220 D) $352 Answer: C Explanation: C) First calculate the APR using an EAR of 14.7% and monthly compounding, which comes to 13.7937 %. Then using a periodic rate of 13.7937 /12, calculate the payment over 48 months that gives a future value (FV) of $14,000 , which is $110.15.

Dan buys a property for $210,000 . He is offered a 30-year loan by the bank, at an interest rate of 8% per year. What is the annual loan payment Dan must make?

A) $18,653.76 B) $22,384.51 C) $26,115.26 D) $29,846.02 Answer: A Explanation: A) Calculate PMT using TVM keys: input PV = 210,000 , N = 30, and interest rate = 8%; PMT = $18,653.76 .

Consider the following timeline detailing a stream of cash flows: 0 = ? 1 = 100 2 = 100 3 = 200 4 = 200 If the current market rate of interest is 8%, then the present value (PV) of this steam of cash flows is closest to: ?

A) $242 B) $581 C) $484 D) $774 Answer: C Explanation: C) PV = 100 /( 1 + 0.08)1 + 100 / (1 + 0.08)2 + 200 / (1 + 0.08)3 + 200 / (1 + 0.08)4 = $484.10

You are considering purchasing a new home. You will need to borrow $290,000 to purchase the home. A mortgage company offers you a 20-year fixed rate mortgage (240 months) at 12% APR (1% month). If you borrow the money from this mortgage company, your monthly mortgage payment will be closest to ________.

A) $2554 B) $4470 C) $3193 D) $5109 Answer: C Explanation: C) PV = 290,000 I=1 N = 240 FV = 0 Compute payment = $3193.15 .

A bank offers a loan that will requires you to pay 7% interest compounded monthly. Which of the following is closest to the EAR charged by the bank?

A) 5.78% B) 8.68% C) 7.23% D) 14.46 % Answer: C

A rich donor gives a hospital $1,040,000 one year from today. Each year after that, the hospital will receive a payment 6% larger than the previous payment, with the last payment occurring in ten yearsʹ time. What is the present value (PV) of this donation, given that the interest rate is 11 %?

A) $3,840,628.87 B) $5,376,880.42 C) $6,913,131.97 D) $7,681,257.74 Answer: D Explanation: D) Payment in 10th year = $1,040,000 × (1 + 0.06)^10 = $1,862,481.6044 ; PV of growth perpetuity in year 10 = $1,862,481.6044 /(0.11 - 0.06 ) = $37,249,632.088 ; PV of this CF at time zero = $13,118,742.261 ; PV of entire CF = $1,040,000 / (0.11 - 0.06) = $20,800,000.000 ; Differenceofthetwocashflows=$20,800,000.000 -$13,118,742.261 = $7,681,257.739

Drew receives an inheritance that pays him $54,000 every three months for the next two years. Which of the following is closest to the present value (PV) of this inheritance if the interest rate is 8.9% (EAR)?

A) $314,366 B) $471,549 C) $392,957 D) $432,000 Answer: C Explanation: C) First calculate the APR with quarterly compounding, which equals 8.62%; then using a periodic interest rate of 8.62/4%, calculate the present value (PV) of an annuity of $54,000 for eight periods.

Since your first birthday, your grandparents have been depositing $1200 into a savings account on every one of your birthdays. The account pays 6% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ________.

A) $37,086.78 A) N = 18 PMT = $1200 I=6 PV = 0 Compute FV = $37,086.78 .

Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $42,000 and you expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be 8% of this yearʹs salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the rate of interest is 9%. The present value (PV) (at age 30) of your retirement savings is closest to ________.

A) $61,303 B) $30,652 C) $42,912 D) $67,433 Answer: A

Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $40,000 and you expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be 8% of this yearʹs salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the rate of interest is 10%. The future value (FV) at retirement (age 65) of your savings is closest to ________.

A) $722,766 B) $1,445,531 C) $1,011,872 D) $1,590,084 Answer: B

Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their childʹs college education. They decide to make deposits into an educational savings account on each of their daughterʹs birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 9%. The parents deposit $2400 on their daughterʹs first birthday and plan to increase the size of their deposits by 7% each year. Assuming that the parents have already made the deposit for their daughterʹs 18th birthday, then the amount available for the daughterʹs college expenses on her 18th birthday is closest to ________.

A) $80,232 B) $160,463 C) $112,324 D) $176,509 Answer: B Explanation: B) FV of a growing annuity

Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $300,000 , or you can lease a truck from the manufacturer for five years for a monthly lease payment of $6000 (paid at the end of each month). Your firm can borrow at 8.00% APR with quarterly compounding. The monthly discount rate that you should use to evaluate the truck lease is closest to ________.

A) 0.5298 % B) 0.7947 % C) 0.6623 % D) 0.6667 % Answer: C Explanation: C) EAR=(1+APR/m)m-1=(1+0.08/4)4-1=0.08243 or 8.243% Monthly rate = (1 + EAR)(1/12) - 1= (1 + 0.08243 )(1/12) - 1 = 0.006623 = 0.6623 %

A 12% APR with bi-monthly compounding is equivalent to an EAR of ________.

A) 11.98% B) 12.50% C) 12.00% D) 12.62% Answer: D Explanation: D) EAR={(1+0.12)/6}6-1=12.62%

The effective annual rate (EAR) for a loan with a stated APR of 11% compounded quarterly is closest to ________.

A) 12.61 % B) 13.75 % C) 11.46% D) 14.90 % Answer: C Explanation: C) EAR=(1+APR/m)^m-1=(1+0.11/4)^4-1=0.1146 or 11.46%

What is the internal rate of return (IRR) of an investment that requires an initial investment of $11,000 today and pays $15,400 in one yearʹs time?

A) 37% B) 44% C) 43% D) 40% Answer: D Explanation: D) Calculate interest rate using TVM keys: input PV = 11,000 , N = 1, and FV = -15,400 ; interest rate = 40%.

How long will it take $50,000 placed in a savings account at 10% interest to grow into $75,000 ?

A) 4.25 years B) 3.25 years C) 5.25 years D) 6.25 years Answer: A Explanation: A) Calculate N using TVM keys: input PV = 50,000 , interest rate = 10%, and FV = 75,000 ; N = 4.25 years.

Faisal has $12,000 in his savings account and can save an additional $3600 per year. If interest rates are 12%, how long will it take his savings to grow to $47,000 ?

A) 4.3 years B) 6.3 years C) 5.3 years D) 7.3 years Answer: C Explanation: C) Calculate N using TVM keys: input PV = $12,000 , interest rate = 12% , PMT = $3600 ; N = 5.3 years.

You are considering investing in a zero-coupon bond that will pay you its face value of $1000 in twelve years. If the bond is currently selling for $496.97 , then the internal rate of return (IRR) for investing in this bond is closest to ________.

A) 5.0% B) 7.1% C) 6.0% D) 8.2% Answer: C Explanation: C) PV = -496.97 FV = 1000 PMT = 0 N = 12 Compute I = 6.0%.

A bank pays interest semiannually with an EAR of 13%.What is the periodic interest rate applicable semiannually ?

A) 5.04% B) 7.56% C) 6.30% D) 12.60 % Answer: C Explanation: C) First convert the EAR to APR with semiannually compounding, which equals 12.60 %; now divide this by 2 to get the periodic interest rate = 6.30 %.

The effective annual rate (EAR) for a savings account with a stated APR of 5% compounded daily is closest to ________.

A) 5.64% B) 6.15% C) 5.13% D) 6.66% Answer: C Explanation: C) EAR=(1+APR/m)m-1=(1+0.05 /365)365-1=0.0513or5.13%

A businessman wants to buy a truck. The dealer offers to sell the truck for either $120,000 now, or six yearly payments of $25,000 . Which of the following is closest to the interest rate being offered by the dealer?

A) 5.8% B) 6.8% C) 7.8% D) 9.8% Answer: B Explanation: B) Calculate interest rate using TVM keys: input PV = $120,000 , N = 6, and PMT = $25,000 ; interest rate = 6.8%.

Consider the following investment activities: Investment APR Compounding A 6.0860% Annual B 5.9320% Daily C 5.9997% Quarterly D 5.9936% Monthly The highest effective rate of return you could earn on any of these investments is closest to ________.

A) 6.0860 % B) 6.1110 % C) 6.1610 % D) 6.1360 % Answer: C Explanation: C) EAR(A)=(1+APR/m)m-1=(1+0.060860/1)1-1=6.0860% EAR(B)=(1+APR/m)m-1=(1+0.059320 /365)365-1=6.1110% EAR (C) = (1 + APR / m)m - 1 = (1 + 0.059997 /4)4 - 1 = 6.1360 % EAR(D)=(1+APR/m)m-1=(1+0.059936 /12)12-1=6.1610%

Consider the following investment alternatives: Investment APR Compounding A 6.3830% Annual B 6.2116% Daily C 6.2834% Quarterly D 6.2744% Monthly The lowest effective rate of return you could earn on any of these investments is closest to ?

A) 6.3830 % B) 6.4080 % C) 6.4330 % D) 6.4580 % Answer: A Explanation: A) EAR (A) = (1 + APR / m)m - 1 = (1 + 0.063830 /1)1 - 1 = 6.3830% EAR(B)=(1+APR/m)m-1=(1+0.062116 /365)365-1=6.4080% EAR (C) = (1 + APR / m)m - 1 = (1 + 0.062834 /4)4 - 1 = 6.4330% EAR(D)=(1+APR/m)m-1=(1+0.062744 /12)12-1=6.4580%

The effective annual rate (EAR) for a loan with a stated APR of 8% compounded monthly is closest to ________.

A) 8.30% B) 9.13% C) 9.96% D) 10.79 % Answer: A

Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $350,000 , or you can lease a truck from the manufacturer for five years for a monthly lease payment of $7000 (paid at the end of each month). Your firm can borrow at 9.00% APR with quarterly compounding. The effective annual rate on your firmʹs borrowings is closest to ________.

A) 9.00% B) 7.45% C) 11.17% D) 9.31% Answer: D D) EAR = (1 + APR / m)m - 1 = (1 + 0.0900 /4)4 - 1 = 0.09308 or 9.31 %

Consider the following investment alternatives: Investment APR Compounding A 6.9030% Annual B 6.6992% Daily C 6.7787% Quarterly D 6.7643% Monthly Which alternative offers you the lowest effective rate of return?

A) Investment A B) Investment B C) Investment C D) Investment D Answer: A Explanation: A) EAR (A) = (1 + APR / m)m - 1 = (1 + 0.069030 /1)1 - 1 = 6.9030 % EAR(B)=(1+APR/m)m-1=(1+0.066992 /365)365-1=6.9280% EAR (C) = (1 + APR / m)m - 1 = (1 + 0.067787 /4)4 - 1 = 6.9530 % EAR(D)=(1+APR/m)m-1=(1+0.067643 /12)12-1=6.9780%

Consider the following investment alternatives: Investment: APR: Compounding: A 6.2200% Annual B 6.0583% Daily C 6.1277% Quarterly D 6.1204% Monthly

A) Investment A B) Investment B C) Investment C D) Investment D Answer: D Explanation: D)EAR(A)=(1+APR/m)m-1=(1+0.062200/1)1-1= 6.2200% EAR(B)=(1+APR/m)m-1=(1+0.060583/365)365-1= 6.2450% EAR (C) = (1 + APR / m)m - 1 = (1 + 0.061277 /4)4 - 1 = 6.2700 % EAR (D) = (1 + APR / m)m - 1 = (1 + 0.061204 /12)12 - 1 = 6.2950 %

Investment X and Investment Y are both growing perpetuities with initial cash flow of $100. Both investments have the same interest rate (r) and cash flows. The present value of Investment X is $5,000, while the present value of Investment Y is $4,000. Which of the following is true?

A) Investment X has a higher growth rate than Investment Y. B) Investment X has a lower growth rate than Investment Y. C) The answer cannot be determined without knowing the interest rate for both investments. D) With the same initial cash flow and the same interest rate, Investment X and Investment Y should have the same present value. Answer: A

What is the effective annual rate (EAR)?

A) It is the interest rate that would earn the same interest with annual compounding. B) It is the ratio of the number of the annual percentage rate to the number of compounding periods per year. C) It is the interest rate for an n-year time interval, where n may be more than one year or less than or equal to one year (a fraction). D) It refers to the cash flows from an investment over a one-year period divided by the number of times that interest is compounded during the year. Answer: A

An animator needs a laptop for audio/video editing, and notices that he can pay $2600 for a Dell XPS laptop, or lease from the manufacturer for monthly payments of $75 each for four years. The designer can borrow at an interest rate of 14% APR compounded monthly. What is the cost of leasing the laptop over buying it outright?

A) Leasing costs $116 more than buying. B) Leasing costs $174 more than buying. C) Leasing costs $145 more than buying. D) Leasing costs $289 more than buying. Answer: C Explanation: C) Using a periodic rate of 14% / 12 per month, calculate the present value (PV) of an annuity of $75 for 48 months; then subtract $2600 to calculate the difference in costs.

Which of the following accounts has the highest EAR?

A) one that pays 5.4% every six months B) one that pays 1.0% per month C) one that pays 9.6% per year D) one that pays 2.4% every three months Answer: B Explanation: B) Calculate the EAR for each choice and pick the highest: A = 11.09%; B= 12.68%; C = 9.60%; D = 9.95%.

Which of the following formulas is INCORRECT? A) PV of a growing annuity = C x 1/r-g (1 - (1+r/1+g)^N) B) PV of an annuity = C x 1/r(1 - 1/(1+r)^N) C) PV of a growing perpetuity = C/r-g D) PV of a perpetuity = C/r

Answer: A

Which of the following statements is FALSE about interest rates? A) As interest rates may be quoted for different time intervals, it is often necessary to adjust the interest rate to a time period that matches that of cash flows. B) The effective annual rate indicates the amount of interest that will be earned at the end of one year. C) The annual percentage rate indicates the amount of simple interest earned in one year. D) The annual percentage rate indicates the amount of interest including the effect of compounding.

Answer: D

If a few intermediate cash flows in valuing a stream of cash flows are zero can we delete those points on the timeline and squeeze the timeline to show only nonzero cash flows?

Every cash flow contains two pieces of information - the nominal value and the time stamp. If we decide to eliminate the zero cash flows from the timeline and concentrate only on the nonzero ones, we will be distorting the time stamp of some nonzero cash flows. Hence, we need to show the timeline in full, including all cash flows zero as well as nonzero.

How do the growth perpetuity results differ with negative and positive growths of similar magnitude assuming everything else remains unchanged?

The denominator in the formula for growth perpetuity plays in important role on the results for negative and positive growths of similar magnitude. A positive growth results in a smaller denominator thereby increasing the present value (PV). Contrarily, a negative growth results in a larger denominator giving a smaller present value (PV).

You are given two choices of investments, Investment A and Investment B. Both investments have the same future cash flows. Investment A has a discount rate of 4%, and Investment B has a discount rate of 5%. Which of the following is true?

The present value of cash flows in Investment A is higher than the present value of cash flows in Investment B.

How do you calculate (mathematically) the present value (PV) of a(n): (a) perpetuity (b) annuity (c) growing perpetuity (d) growingannuity

the formulas.... look on page 151 of the test bank; number 14