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Exam 4: Time Value of Money

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Question 21

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Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?

A) $3,704.02
B) $3,889.23
C) $4,083.69
D) $4,287.87
E) $4,502.26

F) D) and E)
G) B) and C)

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Question 22

Multiple Choice

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Which of the following statements regarding a 15-year (180-month) $225,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

A) The outstanding balance declines at a faster rate in the later years of the loan's life.
B) The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years.
C) Because the outstanding balance declines over time, the monthly payments will also decline over time.
D) Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.
E) The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year.

F) A) and B)
G) A) and D)

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Question 23

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You want to open a sushi bar 3 years from now, and you plan to save $7,000 per year, beginning immediately. You will make 3 deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today?

Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.

If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series.

The store where you bought new home furnishings offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan?

If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate.

Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

What's the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?

Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. You need money today to open a new restaurant, and your uncle offers to give you $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment?

JG Asset Services is recommending that you invest $1,500 in a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures?

A U.S. Treasury bond will 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?

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date.

Which of the following statements regarding a 20-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?

Which of the following bank accounts has the lowest effective annual return?

Which of the following bank accounts has the highest effective annual return?

A $250,000 loan is to be amortized over 8 years, with annual end-of-year payments. Which of these statements is CORRECT?

Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. What is the maximum number of $35,000 withdrawals that he can make and still have at least $25,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)

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

Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years. How much interest would you have to pay in the first year?