## Time Value of Money Problems

1. What is the present value of \$100 received at the end of the first year and \$50 received at the end of the second year and each year after that forever? The discount rate is 10%

2. What present expenditure would be justified by the prospect of saving of \$500 every quarter of the year for 10 years? Assume interest is at 16% compounded quarterly.

3. A person making small loans offers to lend \$200 with the borrower required to pay \$14.44 at the end of each week for 16 weeks to extinguish the debt. By appropriate use of your interest tables, find the approximate interest rate per week. What is the nominal interest rate per annum? What is the effective interest rate per annum?

4. A man arranges to repay a 5 percent \$1000 loan in 10 equal annual installments. After his sixth payment, he borrows another \$1000, also at 5 percent, with the following understanding: he is to pay nothing for the next two years and then repay the balance of the first loan plus the entire second loan in eight equal annual installments starting at the end of the third year. What will this annual payment be?

5. Mr. Smith has received an income contract which provides for 25 decreasing payments to himself, starting with \$1000 at the end of the first year and decreasing by \$20 each year thereafter. Thus his last receipt, at the end of the 25th year, will be \$520. Using interest at 10 percent, compute the uniform annual equivalent of these 25 payments.

6. You are now 25 years old and have just been sold an insurance policy with \$10,000 protection on your life. The cost is \$170 per year. If you live to age 65, the insurance company will pay you \$20,000. Assuming you live to age 65, what portion of the annual cost can be called an investment and what portion of the cost purchased protection? Your minimum acceptable rate of return is 10%. Assume payments are at the end of the year.

7. A \$1000 bond pays 5% simple interest at the end of each year. The bond matures in 20 years at which time the full \$1000 is paid to the bond holder. If the current interest rate is 10%, what amount should one pay for the bond?

8. A bank pays 10% annual interest compounded quarterly. What is the effective annual interest rate?

9. You borrow \$2000 from the Credit Union. The interest rate is 12% annually (nominal). You pay back the bank in 24 equal installments starting one month from the date you borrow the money.

a. What is your monthly payment?

b. How much of your first payment is interest?