Finance 320 Exam 2 Chapters 5,6,7,8,9

The effective annual rate (EAR) for a loan with a stated APR of 8% compounded monthly is closest to? A) 8.30% B) 8.33% C) 8.00% D) 8.24%

A) 8.30% A) EAR = (1 + APR / k)k - 1 = (1 + 0.08 / 12)12 - 1 = 0.083 or 8.3%.

Given the APR of four investments, which offers the highest EAR? Investment A: Rate of Return: 5.7% Compounding: Yearly Investment B: Rate of Return: 5.6% Compounding: Semiannually Investment C: Rate of Return: 5.5% Compounding: Monthly Investment D: Rate of Return: 5.5% Compounding: Weekly

A) Investment A Calculate the EAR for each; A = 5.70%; B = 5.68%; C = 5.64%; D = 5.65%

You are considering purchasing a new truck that will cost you $34,000. The dealer offers you 1.9% APR financing for 48 months (with payments made at the end of the month). Assuming you finance the entire $34,000 and finance through the dealer, your monthly payments will be closest to: A) $708 B) $594 C) $736 D) $1086

C) $736 First we need the monthly interest rate = APR / k = 0.019 / 12 = 0.001583 or 0.1583%. Now: PV = 34000 I = 0.1583 FV = 0 N = 48 Compute PMT = $736.15.

True or False: 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.

False

What is the present value (PV) of an investment that pays $10,000 every year for four years if the interest rate is 7% APR, compounded quarterly?

$33,730 Calculate EAR = 7.1859%; Calculate PV Annuity = $33,730

Which alternative offers you the lowest effective rate of return? Investment A: Rate: 6.25% Compounded: Annually Investment: B Rate:6.10% Compounded: Daily Investment: C Rate: 6.125% Compounded: Quarterly Investment: D Rate: 6.120% Compounded: Monthly

A) Investment A EAR (A) = (1 + APR / k)k - 1 = (1 + 0.0625 / 1)1 - 1 = 0.0625 or 6.250% EAR (B) = (1 + APR / k)k - 1 = (1 + 0.0610 / 365)365 - 1 = 0.06289 or 6.289% EAR (C) = (1 + APR / k)k - 1 = (1 + 0.06125 / 4)4 - 1 = 0.06267 or 6.267% EAR (D) = (1 + APR / k)k - 1 = (1 + 0.0612 / 12)12 - 1 = 0.06295 or 6.300%

True or False: 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

True or False: The annual percentage rate indicates the amount of interest, including the effect of any compounding.

False

A small foundry agrees to pay $250,000 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 $250,000. If the account pays 5.5% APR compounded monthly, how much must be deposited every three months?

$29,770 Calculate the EAR = 5.64%; calculate APR with quarterly compounding = 5.52%; calculate the payment for 8 quarters with $250,000 as future value (FV).

Howard is saving for a long holiday. He deposits a fixed amount every month in a bank account with an EAR of 7.5%. If this account pays interest every month then how much should he save from each monthly paycheck in order to have $10,000 in the account in two years' time?

$388 First calculate the APR using an EAR of 7.5% and monthly compounding, which comes to 7.25%. Then using a periodic rate of 7.25/12, calculate the payment over 24 months that gives a future value (FV) of $10,000

A bank pays interest quarterly with an EAR of 8%. What is the periodic interest rate applicable per quarter?

1.94% First convert the EAR to APR with quarterly compounding, which equals 7.77%; now divide this by 4 to get the periodic interest rate = 1.94%.

A bank offers a loan that will require you to pay 6% interest compounded monthly. Approximately how much EAR charged by the bank?

6.17% EAR = {(1 + APR)/m}m } - 1; EAR = {( 1 + 0.06)/12}12 - 1; 0.0617 × 100 = 6.17%

What is the effective annual rate (EAR)? A) the interest rate that would earn the same interest with annual compounding B) the ratio of the number of the annual percentage rate to the number of compounding periods per year C) the discount 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) the cash flows from an investment over a one-year period divided by the number of times that interest is compounded during the year

A) the interest rate that would earn the same interest with annual compounding

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 it is divided by the number of times it is compounded in a year

A) the quoted interest rate which considered with the compounding period gives the effective interest rate

Given: 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 $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4000 (paid at the end of each month). Your firm can borrow at 6% APR with quarterly compounding. The present value (PV) of the lease payments for the delivery truck is closest to: A) $206,900 B) $207,050 C) $207,680 D) $198,420

B) $207,050 First we need to calculate the monthly discount rate for the lease arrangement. EAR = (1 + APR / k)k - 1 = (1 + 0.06 / 4)4 - 1 = 0.06136 or 6.14% Monthly rate = (1 + EAR)(1/12) - 1= (1.06136)(1/12) - 1 = 0.004975 = 0.4975% Now we can apply the PVA formula to calculate the PV of the lease or by calculator: I = 0.4975 N = 60 (5 years × 12 months/yr) FV = 0 PMT = $4000 Compute PV = 207,051.61.

You are considering purchasing a new automobile that will cost you $28,000. The dealer offers you 4.9% APR financing for 60 months (with payments made at the end of the month). Assuming you finance the entire $28,000 and finance through the dealer, your monthly payments will be closest to: A) $1454 B) $527 C) $467 D) $478

B) $527 First we need the monthly interest rate = APR / k = 0.049 / 12 = 0.004083 or 0.4083%.

Which of the following accounts has the highest EAR? A) one that pays 6.1% every six months B) one that pays 1.0% per month C) one that pays 12.6% per year D) one that pays 3% every three months

B) one that pays 1.0% per month Calculate the EAR for each choice and pick the highest: A = 12.57%; B=12.68%; C = 12.6%; D = 12.55%.

You are purchasing a new home and need to borrow $250,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.25% 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 6.0% 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 $5000 to cover points you are paying the lender. Assuming you do not pay the points and borrow from the mortgage lender at 6.25%, then your monthly mortgage payment (with payments made at the end of the month) will be closest to: A) $1570 B) $1530 C) $1540 D) $1500

C) $1,540 First we need the monthly interest rate = APR / k = 0.0625 / 12 = 0.005208 or 0.5208%. Now: PV = 250,000 (no points) I = 0.5208 FV = 0 N = 360 (30 years × 12 months) Compute PMT = $1539.29.

Drew receives an inheritance that pays him $50,000 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 8.5% (EAR)? A) $354,223 B) $364,309 C) $365,322 D) $400,000

C) $365,322 First calculate the APR with quarterly compounding, which equals 8.24%; then using a periodic interest rate of 8.24/4%, calculate the present value (PV) of an annuity of $50,000 for eight periods.

Given: 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 $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4000 (paid at the end of each month). Your firm can borrow at 6% APR with quarterly compounding. The monthly discount rate that you should use to evaluate the truck lease is closest to: A) 0.487% B) 0.512% C) 0.498% D) 0.500%

C) 0.498% EAR = (1 + APR / k)k - 1 = (1 + 0.06 / 4)4 - 1 = 0.06136 or 6.14% Monthly rate = (1 + EAR)(1/12) - 1= (1.06136)(1/12) - 1 = 0.004975 = 0.498%

The effective annual rate (EAR) for a loan with a stated APR of 10% compounded quarterly is closest to: A) 10.52% B) 10.25% C) 10.38% D) 10.00%

C) 10.38% EAR = (1 + APR / k)k - 1 = (1 + 0.10 / 4)4 - 1 = 0.1038 or 10.38%

The effective annual rate (EAR) for a savings account with a stated APR of 4% compounded daily is closest to: A) 4.00% B) 4.10% C) 4.08% D) 4.06%

C) 4.08% EAR = (1 + APR / k)k - 1 = (1 + 0.04 / 365)365 - 1 = 0.04088 or 4.08%

An 8% APR with monthly compounding is closest to which of the following? A) an EAR of 6.7% B) an EAR of 7.72% C) an EAR of 8.3% D) an EAR of 8.5%

C) Can use the financial calculator or the formula EAR = {(1 + 0.08 / 12}12 - 1 = 8.3%.

A graphic designer needs a laptop for audio/video editing, and notices that they can elect to pay $2900 for a Dell XPS laptop, or lease from the manufacturer for monthly payments of $79 each for four years. The designer can borrow at an interest rate of 7% APR compounded monthly. What is the cost of leasing the laptop over buying it outright?

C) Leasing costs $399 more than buying Using a periodic rate of 7/12% per month, calculate the present value (PV) of an annuity of $79 for 48 months; then subtract $2900 to calculate the advantage of leasing.

A bank offers an account with an APR of 6% and an EAR of 6.09%. How does the bank compound interest for this account? A) weekly compounding B) monthly compounding C) semiannual compounding D) annual compounding

C) Semiannual Compounding Using an APR = 6%, calculate the EAR for the compounding periods given in each choice: A = 6.18%; B = 6.17%; C = 6.09%; D = 6%.

Given: 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 $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4000 (paid at the end of each month). Your firm can borrow at 6% APR with quarterly compounding. The effective annual rate on your firm's borrowings is closest to: A) 6.00% B) 6.24% C) 6.17% D) 6.14%

D) 6.14% EAR = (1 + APR / k)k - 1 = (1 + 0.06 / 4)4 - 1 = 0.06136 or 6.14%

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 $4200 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 $8642 less than the cost of the oven. C) Lease, since the present value (PV) of the lease is $2212 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.

D) Buy, since the present value (PV) of the lease is $32,108 more than the cost of the oven. Calculate PV lease payments = $212,108; subtract $180,000 to get $32,108.

Which alternative offers you the highest effective rate of return? Investment A: Rate: 6.25% Compounded: Annually Investment: B Rate:6.10% Compounded: Daily Investment: C Rate: 6.125% Compounded: Quarterly Investment: D Rate: 6.120% Compounded: Monthly

D) Investment D EAR (A) = (1 + APR / k)k - 1 = (1 + 0.0625 / 1)1 - 1 = 0.0625 or 6.250% EAR (B) = (1 + APR / k)k - 1 = (1 + 0.0610 / 365)365 - 1 = 0.06289 or 6.289% EAR (C) = (1 + APR / k)k - 1 = (1 + 0.06125 / 4)4 - 1 = 0.06267 or 6.267% EAR (D) = (1 + APR / k)k - 1 = (1 + 0.0612 / 12)12 - 1 = 0.06295 or 6.300%

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 investment will be for a long period of time.

D) The investment will be for a long period of time.

Which of the following statements is FALSE? A) Because 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 our 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

False: D) The annual percentage rate indicates the amount of interest including the effect of compounding. True: A) Because 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 our 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.

The lowest effective rate of return you could earn on any of these investments is closest to: Investment A: Rate: 6.25% Compounded: Annually Investment: B Rate:6.10% Compounded: Daily Investment: C Rate: 6.125% Compounded: Quarterly Investment: D Rate: 6.120% Compounded: Monthly

Investment A: 6.250% EAR (A) = (1 + APR / k)k - 1 = (1 + 0.0625 / 1)1 - 1 = 0.0625 or 6.250% EAR (B) = (1 + APR / k)k - 1 = (1 + 0.0610 / 365)365 - 1 = 0.06289 or 6.289% EAR (C) = (1 + APR / k)k - 1 = (1 + 0.06125 / 4)4 - 1 = 0.06267 or 6.267% EAR (D) = (1 + APR / k)k - 1 = (1 + 0.0612 / 12)12 - 1 = 0.06295 or 6.300%

The highest effective rate of return you could earn on any of these investments is closest to: Investment A: Rate: 6.25% Compounded: Annually Investment: B Rate:6.10% Compounded: Daily Investment: C Rate: 6.125% Compounded: Quarterly Investment: D Rate: 6.120% Compounded: Monthly

Investment D: 6.300% EAR (A) = (1 + APR / k)k - 1 = (1 + 0.0625 / 1)1 - 1 = 0.0625 or 6.250% EAR (B) = (1 + APR / k)k - 1 = (1 + 0.0610 / 365)365 - 1 = 0.06289 or 6.289% EAR (C) = (1 + APR / k)k - 1 = (1 + 0.06125 / 4)4 - 1 = 0.06267 or 6.267% EAR (D) = (1 + APR / k)k - 1 = (1 + 0.0612 / 12)12 - 1 = 0.06295 or 6.300%