Time Value Money
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1. Future Values. You deposit $1,000 in your bank account. If the bank pays 4 percent simple interest, how much will you accumulate in your account after 10 years? What if the bank pays compound interest? How much of your earnings will be interest on interest?
2. Calculating Interest Rate. Find the annual interest rate.
Present Value Future Value Time Period
100 115.76 3 years
200 262.16 4 years
100 110.41 5 years
3. Present Values. What is the present value of the following cash-flow stream if the interest rate is 5 percent?
Year Cash Flow
1 $200
2 $400
3 $300
4. Calculating Interest Rate. Lenny Loanshark charges "one point" per week (that is, 1 percent per week) on his loans. What APR must he report to consumers? Assume exactly 52 weeks in a year. What is the effective annual rate?
5. Loan Payments. If you take out an $8,000 car loan that calls for 48 monthly payments at an APR of 10 percent, what is your monthly payment? What is the effective annual interest rate on the loan?
6. Annuity Value. Your landscaping company can lease a truck for $8,000 a year (paid at yearend) for 6 years. It can instead buy the truck for $40,000. The truck will be valueless after 6 years. If the interest rate your company can earn on its funds is 7 percent, is it cheaper to buy or lease?
7. Annuity Due. A store offers two payment plans. Under the installment plan, you pay 25 percent down and 25 percent of the purchase price in each of the next 3 years. If you pay the entire bill immediately, you can take a 10 percent discount from the purchase price. Which is a better deal if you can borrow or lend funds at a 6 percent interest rate?
8. Amortizing Loan. You take out a 30-year $100,000 mortgage loan with an APR of 8 percent and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan?
9. Perpetuities. A local bank will pay you $100 a year for your lifetime if you deposit $2,500 in the bank today. If you plan to live forever, what interest rate is the bank paying?
10. Applying Time Value. You invest $1,000 today and expect to sell your investment for $2,000 in 10 years.
a. Is this a good deal if the discount rate is 5 percent?
b. What if the discount rate is 10 percent?
11. Calculating Interest Rate. A store will give you a 3 percent discount on the cost of your purchase if you pay cash today. Otherwise, you will be billed the full price with payment due in 1 month. What is the implicit borrowing rate being paid by customers who choose to defer payment for the month?
12. Real versus Nominal Dollars. Your consulting firm will produce cash flows of $100,000 this year, and you expect cash flow to keep pace with any increase in the general level of prices. The interest rate currently is 8 percent, and you anticipate inflation of about 2 percent.
a. What is the present value of your firm's cash flows for Years 1 through 5?
b. How would your answer to (a) change if you anticipated no growth in cash flow?
13. Rule of 72. Using the Rule of 72, if the interest rate is 8 percent per year, how long will it take for your money to quadruple in value?
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Time Value Money
1. Future Values. You deposit $1,000 in your bank account. If the bank pays 4 percent simple interest, how much will you accumulate in your account after 10 years? What if the bank pays compound interest? How much of your earnings will be interest on interest?
(1,000 x 0.04 x 10) + 1,000 = 1,400
FV = 1,000(1.04)10
FV = 1,480.24
Interest on interest = 1,480.24 - 1,400 = 80.24
2. Calculating Interest Rate. Find the annual interest rate.
Present Value Future Value Time Period
100 115.76 3 years
200 262.16 4 years
100 110.41 5 years
115.76 = 100(1 + r)3
r = 5%
262.16 = 200(1 + r)4
r = 7%
110.41 = 100(1 + r)5
r = 2%
3. Present Values. What is the present value of the following cash-flow stream if the interest rate is 5 percent?
Year Cash Flow
1 $200
2 $400
3 $300
Present value = 200/1.05 + 400/(1.05)2 + 300/1.05)3
= 190.48 + 362.81 + 259.15
= 812.44
4. Calculating Interest Rate. Lenny Loanshark charges "one point" per week (that is, 1 percent per week) on his loans. What APR must he report to consumers? Assume exactly 52 weeks in a year. What is the effective annual rate?
Effective annual interest rate = (1 + R / P)P - 1 ,
where R is the nominal rate and P is the number of compounding periods.
R = 1% x 52 = 52%
EAR = (1 + 0.52/52)52 - 1 = 67.77%
5. Loan Payments. If you take out an $8,000 ...
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