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Exam 4: Time Value of Money

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Question 61

True/False

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The present value of a future sum decreases as either the discount rate or the number of periods per year increases.

A) True
B) False

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Question 62

Multiple Choice

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Suppose a Government of Canada bond will pay $2,500 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today?

A) $1,928.78
B) $2,030.30
C) $2,131.81
D) $2,238.40

E) B) and D)
F) A) and D)

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Question 63

Multiple Choice

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A homeowner just obtained a 30-year amortized mortgage loan for $150,000 at a nominal annual rate of 6.5%, with 360 end-of-month payments. What percentage of the total payments made during the first 3 months will go toward payment of interest?

Your aunt is about to retire, and she wants to buy an annuity that will supplement her income by $65,000 per year for 25 years, beginning a year from today. The going rate on such annuities is 6.25%. How much would it cost her to buy such an annuity today?

Suppose you take out a $10,000 loan at a 6% nominal annual rate. The terms of the loan require you to make 12 equal end-of-month payments each year for 4 years, and then an additional final (balloon) payment of $4,000 at the end of the last month. What will your equal monthly payments be?

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate. If you must make monthly payments, which amounts to monthly compounding, what is the effective annual rate?

Merchants Bank offers to lend you $30,000 at a nominal rate of 6.0%, simple interest, with interest paid quarterly. Gold Coast Bank offers to lend you the $30,000, but it will charge 7.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks?

You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of Years 4 through 7. Breck is essentially riskless, so you are confident the payments will be made, and you regard 8% as an appropriate rate of return on low risk 7-year loans. What cash flow must the investment provide at the end of each of the final four years, that is, what is X?

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal.

Pace Co. borrowed $25,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month?

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan).

Your father now has $1,000,000 invested in an account that pays 9.00%. He expects inflation to average 3%, and he wants to make annual constant dollar (real) beginning-of-year withdrawals over each of the next 20 years and end up with a zero balance after the 20th year. How large will his initial withdrawal (and thus constant dollar [real] withdrawals) be?

A Canada government bond promises to pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is correct?

East Coast Bank offers to lend you $25,000 at a nominal rate of 7.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Midwest Bank also offers to lend you the $25,000, but it will charge an annual rate of 8.3%, with no interest due until the end of the year. What is the difference in the effective annual rates charged by the two banks?

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?

How much would $5,000 due in 50 years be worth today if the discount rate were 7.5%?

Your friend just won the lottery. She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming 1 year from today. What rate of return is built into the annuity?