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Exam 4: Time Value of Money

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Question 51

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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 would your payments be?

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

E) None of the above
F) B) and C)

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Question 52

Multiple Choice

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You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?

A) 7.62%
B) 8.00%
C) 8.40%
D) 8.82%

E) None of the above
F) A) and D)

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Question 53

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When inputting information into a financial calculator, one of the cash flow components must be negative since the calculator is set up to solve an equation equal to zero.

What's the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly?

Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is correct?

You plan to invest in securities that pay 9.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment account to grow to $9,140.20?

An investment costs $1,000 (CF at t = 0) and is expected to produce cash flows of $75 at the end of each of the next 5 years, then an additional lump sum payment of $1,000 at the end of the 5th year. What is the expected rate of return on this investment?

Your uncle has $500,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $40,000 at the beginning of each year, beginning immediately. How many years will it take to exhaust his funds, i.e., run the account down to zero?

Your aunt is about to retire, and she wants to buy an annuity that will provide her with $65,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 6.25%. How much would it cost her to buy the annuity today?

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

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?

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?

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 6.5%?

What is the PV of an annuity due with 10 payments of $2,700 at an interest rate of 6.5%?

A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is correct?

Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures?

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.

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

Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year. What is the effective annual rate on the loan?

John and Daphne are saving for their daughter Ellen's university education. Ellen is now 10 years old and will be entering university 8 years from now (t = 8) . University tuition and expenses at City U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. John and Daphne expect Ellen to graduate in four years. (If Ellen wants to go to graduate school, she will be on her own.) Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11) . So far, John and Daphne have accumulated $15,000 in the university savings account. Their long-run financial plan is to add an additional $5,000 at the beginning of each of the next 4 years (at t = 0, 1, 2, and 3) . Then they plan to make four equal annual contributions at the end of each of the following five years (t = 4, 5, 6, 7, and 8) . They expect their investment account to earn 9%. How large must the annual payments be at t = 4, 5, 6, 7, and 8 to meet Ellen's anticipated university costs?