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Exam 28: Time Value of Money

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Question 81

Multiple Choice

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

A) $58,601
B) $61,686
C) $64,932
D) $68,179
E) $71,588

F) C) and D)
G) None of the above

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Question 82

Multiple Choice

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A perpetuity pays $85 per year and costs $950. What is the rate of return?

A) 8.95%
B) 9.39%
C) 9.86%
D) 10.36%
E) 10.88%

F) C) and D)
G) A) and C)

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Question 83

Multiple Choice

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

Scott and Linda have been saving to pay for their daughter Casie's college education. Casie just turned 10 at (t = 0) , and she will be entering college 8 years from now (at t = 8) . College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 yearsσif she takes longer or 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) .σσSo far, Scott and Linda 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 Casie's anticipated college costs?

When a loan is amortized, a relatively low percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage increases in the loan's later years.

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.

You would like to travel in South America 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now?

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?

Which of the following statements is CORRECT?

What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?

Your bank account pays a 5% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

A salt mine you inherited will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the mine is 7.5%, how much should you ask for it if you decide to sell it?

Partners Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. An offer to lend you the $50,000 also comes from Community Bank, but it will charge 6.0%, 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 hoping to buy a new boat 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?

Your cousin will sell you his coffee shop for $250,000, with "seller financing," at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be?

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?

Wildwoods, Inc. earned $1.50 per share five years ago. Its earnings this year were $3.20. What was the growth rate in earnings per share (EPS) over the 5-year period?

Your uncle just won the weekly lottery, receiving $375,000, which he invested at a 7.5% annual rate. He now has decided to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. What is the maximum number of whole payments that can be withdrawn before the account is exhausted, i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.)

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

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. By how much would you reduce the amount you owe in the first year?