Finance Chapter 5 The effective monthly discount rate that you shoul

Corporate Finance, 4e (Berk / DeMarzo)

Chapter 5 Interest Rates

5.1 Interest Rate Quotes and Adjustments

1) 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 compounding.

2) Which of the following equations is INCORRECT?

A) – 1= APR

B) Equivalent n–Period Discount Rate = (1 + r)n – 1

C) 1 + EAR =

D) Interest Rate per Compounding Period =

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

A) 7.72%

B) 8.00%

C) 8.30%

D) 8.66%

4) The effective annual rate (EAR) for a loan with a stated APR of 10% compounded quarterly is closest

to:

A) 9.65%

B) 10.00%

C) 10.38%

D) 12.50%

5) The effective annual rate (EAR) for a savings account with a stated APR of 4% compounded daily

(use 365 day year) is closest to:

A) 3.92%

B) 4.00%

C) 4.08%

D) 14.60%

Use the table for the question(s) below.

Consider the following investment alternatives:

Investment

Rate

Compounding

A

6.25%

Annual

B

6.10%

Daily

C

6.125

Quarterly

D

6.120

Monthly

6) Which alternative offers you the highest effective rate of return?

A) Investment A

B) Investment B

C) Investment C

D) Investment D

7) Which alternative offers you the lowest effective rate of return?

A) Investment A

B) Investment B

C) Investment C

D) Investment D

8) The highest effective rate of return you could earn on any of these investments is closest to:

A) 6.250%

B) 6.267%

C) 6.295%

D) 6.310%

9) The lowest effective rate of return you could earn on any of these investments is closest to:

A) 6.150%

B) 6.250%

C) 6.289%

D) 6.300%

Use the information for the question(s) below.

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.

10) The effective annual rate on your firm’s borrowings is closest to:

A) 6.00%

B) 6.14%

C) 6.25%

D) 6.30%

11) The effective annual rate for a credit card that charges a 19.9% APR compounded daily is closest to:

A) 18.15%

B) 19.9%

C) 22.0%

D) 24.2%

12) The effective annual rate for a certificate of deposit that pays 3.9% APR compounded monthly is

closest to:

A) 3.83%

B) 3.90%

C) 3.97%

D) 4.04%

13) Wesley Mouch’s auto loan requires monthly payments and has an effective annual rate of 6.43%.

The APR on this auto loan is closest to:

A) 6.00%

B) 6.25%

C) 6.50%

D) 6.62%

14) Interest on James Taggart’s credit card balances are compounded daily at an effect annual rate of

14.91%. The APR on his credit card is closest to:

A) 13.90%

B) 13.95%

C) 14.91%

D) 16.08%

15) Suppose the interest rate is 9% APR with monthly compounding. Then the present value of an

annuity that pays $250 every three months for the next five years is closest to:

A) $2280

B) $3985

C) $3990

D) $3995

16) Floyd Ferris invested $3000 into an account five years ago. Today his account has grown to have a

balance of $3927.50. Given that his account offered monthly compounding of interest, the APR on this

account is closest to:

A) 5.00%

B) 5.25%

C) 5.40%

D) 5.54%

Use the information for the question(s) below.

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.

17) The effective monthly discount rate that you should use to evaluate the truck lease is closest to:

A) 0.487%

B) 0.498%

C) 1.500%

D) 1.535%

18) The present value of the lease payments for the delivery truck is closest to:

A) $206,900

B) $207,050

C) $207,680

D) $198,420

19) 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) $457

20) 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) $725

C) $736

D) $1086

Use the information for the question(s) below.

You are in the process of purchasing a new automobile that will cost you $27,500. The dealership is

offering you either a $2500 rebate (applied toward the purchase price) or 1.9% financing for 48 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 6.5% for 48 months.

21) If you take the $2500 rebate and finance your new car through your credit union your monthly

payments will be closest to:

A) $520

B) $573

C) $593

D) $799

22) If you forgo the $2500 rebate and finance your new car through the dealership your monthly

payments (with payments made at the end of the month) will be closest to:

A) $520

B) $573

C) $595

D) $799

Use the information for the question(s) below.

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 2 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.

23) Assuming you don’t 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) $694

B) $708

C) $1540

D) $1600

24) Assuming you pay the points and borrow from the mortgage lender at 6.00%, then your monthly

mortgage payment (with payments made at the end of the month) will be closest to:

A) $708

B) $1530

C) $1540

D) $1600

Use the information for the question(s) below.

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 5.9% APR. You monthly payments are $617.16 and you have just

made your 24th monthly payment on your SUV.

25) The amount of your original loan is closest to:

A) $14,808

B) $22,212

C) $32,000

D) $37,020

26) 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) $14,808

B) $20,300

C) $22,212

D) $32,000

Use the information for the question(s) below.

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.

27) Should you purchase the delivery truck or lease it? Why?

28) You are in the process of purchasing a new automobile that will cost you $25,000. The dealership is

offering you either a $1000 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 $2000 rebate and

finance through your credit union or forgo the rebate and finance through the dealership at the lower

3.9% APR?

29) 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 1 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

$3250 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 1 point and borrowing at 6.25%

APR or just taking out the loan at 6.5% without any points?

Use the information for the question(s) below.

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 5.9% APR. You monthly payments are $617.16 and you have just

made your 24th monthly payment on your SUV.

30) Assuming that you have made all of the first 24 payments on time, then how much interest have you

paid over the first two years of your loan?

5.2 Application: Discount Rates and Loans

1) Hugh Akston took out a 30-year mortgage with an EAR of 5.9%. If Hugh borrowed $300,000 to buy

his home, then his monthly payment will be closest to:

A) $835

B) $1750

C) $1780

D) $10,240

Use the following information to answer the question(s) below.

Dagny Taggart has just purchased a home and taken out a $400,000 mortgage. The mortgage has a 30–

year term with monthly payments and has an APR of 5.4%.

2) Dagny’s monthly payments are closest to:

A) $1110

B) $1800

C) $2215

D) $2245