Corporate Finance, 3e (Berk/DeMarzo) Chapter 5 Interest Rates

Corporate Finance, 3e (Berk/DeMarzo)

Chapter 5 Interest Rates

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5.1 Interest Rate Quotes and Adjustments

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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.

Answer: D

Diff: 1

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Conceptual

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Which of the following equations is INCORRECT?

A)

- 1= APR

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

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C) 1 + EAR =

D) Interest Rate per Compounding Period =

Answer: A Diff: 2 Section: 5.1 Interest Rate Quotes and Adjustments Skill: Conceptual

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

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closest to: A) 7.72% B) 8.00% C) 8.30% D) 8.66% Answer: C

k

12

Explanation: C) EAR = (1 + APR/k) - 1 = (1 + .08/12) - 1 = .083 or 8.3%

Diff: 1

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

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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%

Answer: C

k

4

Explanation: C) EAR = (1 + APR/k) - 1 = (1 + .10/4) - 1 = .1038 or 10.38%

Diff: 1

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

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Explanation: C) First we need the monthly interest rate = APR/k = .059/12 = .004917 or 0.4917%.

60

PV = 617.16 ? (1/0.004917) ? (1 - 1/(1.004917 )) = $31,999.86

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

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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?

Answer: Pay the points!

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Points (6.25% APR)

First we need the monthly interest rate = APR/k = .0625/12 = .00520833 or .5208%.

Now:

PV = 328250 ( 325,000 + 1 point)

I = .5208

FV = 0

N = 360 (30 years ? 12 months)

Compute PMT = $2,021.01

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No Points First we need the monthly interest rate = APR/k = .065/12 = .005417 or .5417%.

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Now: PV = 325000 (no points) I = .5417 FV = 0 N = 360 (30 years ? 12 months) Compute PMT = $2,054.22

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Since $2,021.01 < $2,054.22, pay the points! Diff: 3 Section: 5.1 Interest Rate Quotes and Adjustments Skill: Analytical

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