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Exam 4: Time Value of Money

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Question 1

Multiple Choice

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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?

A) 0.93%
B) 0.77%
C) 0.64%
D) 0.54%

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

Correct Answer

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D

Question 2

Multiple Choice

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Which of the following statements best describes time lines?

A) A time line is not meaningful unless all cash flows occur annually.
B) Time lines are useful for visualizing complex problems prior to doing actual calculations.
C) Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly.
D) Time lines can be constructed only for annuities where the payments occur at the ends of the periods, i.e., for ordinary annuities.

E) B) and C)
F) A) and B)

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Question 3

Multiple Choice

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Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. How much interest would you have to pay in the first year?

Your child's orthodontist 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?

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?

Suppose a Government of Canada bond promises to pay $1,000 five years from now. If the going interest rate on 5-year government bonds is 5.5%, how much is the bond worth today?

You are considering investing in a bank account that pays a nominal annual rate of 6%, compounded monthly. If you invest $5,000 at the END of each month, how many months will it take for your account to grow to $200,000? Round fractional years up.

You have a chance to buy an annuity that pays $550 at the BEGINNING of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the BEGINNING of each of the next 20 years?

You want to go to Europe 5 years from now, and you can save $3,100 per year, BEGINNING IMMEDIATELY. You plan to deposit the funds in a mutual fund that you expect to return 8.5% per year. Under these conditions, how much will you have just after you make the fifth deposit, 5 years from now?

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?

You are analyzing the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?

Which of the following statements is correct?

Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. 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?

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. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

Your uncle has $375,000 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. How many years will it take to exhaust his funds, i.e., run the account down to zero?

Credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 18.00%, with interest paid monthly, what is the card's EFF percentage?

How many years would it take $50 to triple if it were invested in a bank that pays 3.8% per year?

You own an oil well that will pay you $30,000 per year for 10 years, with the first payment being made today. If you think a fair return on the well is 8.5%, how much should you ask for if you decide to sell it?

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?