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Exam 5: The Value of Money

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Question 31

Multiple Choice

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

A) An account that pays 8% nominal interest with monthly compounding.
B) An account that pays 8% nominal interest with annual compounding.
C) An account that pays 7% nominal interest with daily (365-day) compounding.
D) An account that pays 7% nominal interest with monthly compounding.
E) An account that pays 8% nominal interest with daily (365-day) compounding.

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

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Question 32

Multiple Choice

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John and Daphne are saving for their daughter Ellen's college education. Ellen 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 years if 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) . 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?

A) $1,965.21
B) $2,068.64
C) $2,177.51
D) $2,292.12
E) $2,412.76

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

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Question 33

Multiple Choice

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Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?

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

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

You just inherited some money, and a broker offers to sell you an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

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?

You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round fractional months up.

Your uncle will sell you his bicycle 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?

You want to go to Europe 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?

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?

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

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

Suppose you are buying your first condo for $145,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be?

You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4. What rate of return would you earn if you bought this asset?

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

A $150,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT?

Last year Thomson Inc's earnings per share were $3.50, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Thomson's EPS to triple?

How much would $20,000 due in 50 years be worth today if the discount rate were 7.5%?

Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.