FIN302 ch.5
A 12% APR with bi-monthly compounding is equivalent to an EAR of ________.
D) 12.62% D) EAR = {(1 + 0.12) / 6}6 - 1 = 12.62%
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 ________.
D) 7.0% 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%
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.
The yield curve is typically ________.
B) upward sloping
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?
NPV = -$2,500 + $1,000 / (1.05)1 + $1,000 / (1.046)3 + $1,000 / (1.045)5 = $128.62
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 A) Calculate EAR = 5.0945 %; Calculate PV Annuity = $353,818
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.
Market forces determine interest rates based ultimately on the willingness of individuals, banks, and firms to borrow, save, and lend.
TRUE
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.
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 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 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 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.
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 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).
The present value (PV) of receiving $1100 per year with certainty at the end of the next three years is closest to ________.
A) $3010 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 A) Calculate the PV annuity of $770 for 48 months at 5.00/12 = 0.416667 %, which = $33,436 .
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 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
In 2009, U.S. Treasury yielded 0.1%, while inflation was 2.7%. What was the real rate in 2009?
A) -2.6% 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% A) The percentage of outstanding principal paid is the monthly periodic interest rate = 6.75/12 = 0.56%.
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?
B) 8% B) $5508 - $5100 = $408 ; $408 / $5100 = 0.08 or 8%
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 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.
The lowest effective rate of return you could earn on any of these investments is closest to ________.
A) 6.3830% 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%
What is the real interest rate given a nominal rate of 8.9% and an inflation rate of 1.9%?
A) 6.9% A) (0.089 ) / (1+ 0.019 ) - 1 = 0.06869 ;real rate = 6.869%
The effective annual rate (EAR) for a loan with a stated APR of 8% compounded monthly is closest to ________.
A) 8.30% A) EAR = (1 + APR / m)m - 1 = (1 + 0.08/12)12 - 1 = 0.0830 or 8.30%.
The table above shows the rate of return (APR) for four investment alternatives. Which offers the highest EAR?
A) Investment A A) Calculate the EAR for each; A = 6.0%; B = 5.99%; C = 5.96%; D = 5.86%.
Which alternative offers you the lowest effective rate of return?
A) Investment A 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%
What is the effective annual rate (EAR)?
A) It is the interest rate that would earn the same interest with annual compounding.
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.
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
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
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.
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.
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
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 ________.
B) 9.4% B) nominal = (1 + inflation)(1 + real) - 1 = (1 + 0.073 )(1 + 0.02) - 1 = 0.0945or 9.4%
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.
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?
B) $10,311.34 B) Calculate bimonthly payment when PV of ordinary annuity = $1,724,000 , periodic interest = 7.70/24%, and number of periods = 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 ________.
B) $12,727 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 .
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 ________.
B) $1676 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
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 ________.
B) $20,000 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
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 ________.
B) $238,132 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 or 8.031% 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 .
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 ________.
B) $460 B) First we need the monthly interest rate = APR / m = 0.0400 / 12 = 0.003333 or 0.3333 %. Now: PV =$25,000 I = 0.3333 FV = 0 N = 60 Compute PMT = $460.41
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?
B) 57.07 months 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.
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.
B) Only II is true.
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?
B) The monthly payment will decrease by $104.79 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
Which of the following accounts has the highest EAR?
B) one that pays 1.0% per month B) Calculate the EAR for each choice and pick the highest: A = 11.09 %; B= 12.68 %; C = 9.60%; D = 9.95%.
What, typically, is used to calculate the opportunity cost of capital on a risk-free investment?
B) the interest rate on U.S. Treasury securities with the same term
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?
B) when short-term and long-term interest rates vary widely
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?
C) $1316.69 C) Calculate the PMT when PV of ordinary annuity = $50,000 , periodic interest = 12/12%, and number of periods = 48.
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?
C) $220 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.
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 ________.
C) $2218 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?
C) $306,206 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 .
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?
C) semiannual compounding 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%.
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?
C) $31,195 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.
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)?
C) $392,957 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.
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 ________.
C) $573 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 .
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?
C) $71,521 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?
C) $72,416 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 .
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 ________.
C) 0.6623% 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 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?
C) 10 years C) Calculate N when PV of ordinary annuity = $68,000 , periodic interest = 6.3/12%, and monthly payments = $765.22 . N = 156 periods; years = 13 years.
A 10% APR with quarterly compounding is equivalent to an EAR of ________.
C) 10.38% C) EAR = (1 + 0.10 / 4)4 - 1 = 10.38%
The effective annual rate (EAR) for a loan with a stated APR of 11% compounded quarterly is closest to ________.
C) 11.46% C) EAR = (1 + APR / m)m - 1 = (1 + 0.11/4)4 - 1 = 0.1146 or 11.46%
The effective annual rate (EAR) for a savings account with a stated APR of 5% compounded daily is closest to ________.
C) 5.13% C) EAR = (1 + APR / m)m - 1 = (1 + 0.05 / 365)365 - 1 = 0.0513 or 5.13%
The highest effective rate of return you could earn on any of these investments is closest to ________.
C) 6.1610% 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%
A bank pays interest semiannually with an EAR of 13%. What is the periodic interest rate applicable semiannually ?
C) 6.30% 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%.
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?
C) 7.23% C) EAR = {(1 + APR) / m}m - 1; EAR = {(1 + 0.07) / 12}12 - 1; 0.0723 × 100 = 7.23%
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?
C) 7.25% 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%.
Inflation is calculated as the rate of change in the _______.
C) Consumer Price Index
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?
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.
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?
C) Leasing costs $145 more than buying. 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.
A(n) 12% APR with monthly compounding is closest to ________.
C) an EAR of 12.68% C) EAR = {(1 + 0.12) / m}m - 1 = 12.68 %.
What is the shape of the yield curve and what expectations are investors likely to have about future interest rates?
C) inverted; lower
Which of the following yield curves would most likely predict a downturn in the economy?
D
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?
D) $100,251 D) Current Mortgage Payment: P/Y = 12, N = 360, I/Y = 6.20,PV = $206,000 , Solve for PMT = 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
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?
D) $1512.22 D) Calculate the PMT when PV of ordinary annuity = $52,000 , periodic interest = 3/12%, and number of periods = 36.
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?
D) $22,639 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 .
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?
D) $95,647 D) Using FV = $100,000 , find the present value (PV) at 2.25% for 2 years.
he 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 ________.
D) -$114.21 D) NPV = -4320 + 1600 / (1.05)1 +1600 / (1.046)3 + 1600 / (1.045)5 = -$114.21
In 2007, interest rates were about 4.5% and inflation was about 2.8%. What was the real interest rate in 2007?
D) 1.65% D) 1.045 / 1.028 = 1.0165; real rate = 1.65%
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?
D) 122 months 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.
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 ________.
D) 4.51% 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 or 4.51%
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 ?
D) 7.8% APR for 72 months D) Calculate N when PV of ordinary annuity = $19,000 - $2,000 - $800 = $16,200 , periodic interest = 7.8/12%, and monthly payments = $282 .
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 ________.
D) 9.31% D) EAR = (1 + APR / m)m - 1 = (1 + 0.0900 /4)4 - 1 = 0.09308 or 9.31%
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?
D) Buy, since the present value (PV) of the lease is $32,108 more than the cost of the oven. D) Calculate PV lease payments = $212,108; subtract $180,000 to get $32,108.
Which of the following statements is FALSE?
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
Which alternative offers you the highest effective rate of return?
D) Investment D 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%
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?
D) It will make it less attractive, since it will decrease the investmentʹs net present value (NPV).
Which of the following statements is FALSE about interest rates?
D) The annual percentage rate indicates the amount of interest including the effect of compounding.
Which of the following reasons for considering long-term loans inherently more risky than short-term loans is most accurate?
D) The loan values are very sensitive to changes in market interest rates.
Historically, why were high inflation rates associated with high nominal interest rates?
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
Which of the following computes the growth in purchasing power?
D) growth of money / growth of prices
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.
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.
FALSE
The real interest rate is the rate of growth of oneʹs purchasing power due to money invested.
FALSE
The term opportunity 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.
FALSE
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?
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 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.
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?
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!
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
Quality adjustments to changes in the CPI most often result in reductions to the inflation rate calculated from it.
TRUE
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.