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Exam 5: Time Value of Money

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Question 21

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What's the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly?

A) $1,537.69
B) $1,618.62
C) $1,699.55
D) $1,784.53
E) $1,873.76

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

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Question 22

Multiple Choice

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You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now?

A) $15,234.08
B) $16,035.87
C) $16,837.67
D) $17,679.55
E) $18,563.53

F) A) and B)
G) A) and C)

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Question 23

Multiple Choice

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Sue now has $125. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding?

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?

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

Your grandmother just died and left you $100,000 in a trust fund that pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?

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

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment?

You plan to analyze 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?

Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

John and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 (at t = 0) So far, John and Daphne have accumulated $15,000 in their college savings account (at t = 0) . Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4) . Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen's anticipated college costs?

Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today?

Which of the following statements is CORRECT?

Jose now has $500. How much would he have after 6 years if he leaves it invested at 5.5% with annual compounding?

Midway through the life of an amortized loan, the percentage of the payment that represents interest could be equal to, less than, or greater than to the percentage that represents repayment of principal. The proportions depend on the original life of the loan and the interest rate.

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

Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. How much will you have when the CD matures?

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

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?

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 smaller the percentage of the payment that will be a repayment of principal.