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# Effective Rate and Present Value of Bonds

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Find the accumulated amount A if \$3100.00 is invested at the interest rate of 7.855%/year compounded daily for 12 years.

Find the effective rate corresponding to a 3.95%/year compounded daily.

Find the present value of \$75,000 due in 5 yr at 9.3%/year compounded monthly.

David owns \$30,000 of 15-yr public bonds. The bonds pay interest every 3 months at the rate of 7.75%/year (simple interest).

a) How much interest will David receive from the bonds every three months

b) How much interest will David receive over the life of the bonds?

Anthony invested a sum of money five years ago in a savings plan that has since paid interest at the rate of 7.65%/yr compounded quarterly. His investment is now worth \$22,289.22. How much did Anthony originally invest?

A utility company in a western city of the United States expects the consumption of electricity to increase by 6.55% per year during the next two decades. If consumption does increase at this rate, find the amount by which the utility company will have to increase its generating capacity to meet the needs of the area 20 years from now.

#### Solution Summary

This provides examples of working with interest, including effective rate, present value, bonds, and investments.

\$2.19

## Time value of money: Present value, future value, deposits, bonds, compounding

Please provide detailed explanations and step by step processes for understanding the problems.

Problem 2-2

Use equations and a financial calculator to find the following values.

a) An initial \$500.00 compounded for 10 years at 6 percent.
b) An initial \$500.00 for 10 years at 12 percent.
c) The present value of \$500.00 due in 10 years at a 6 percent discount rate.
d) The present value of \$1,552.90 due in 10 years at a 12 percent discount rate and at a 6 percent rate. Give a verbal definition of the term present value, and illustrate it using a time line with data from this problem. As a part of your answer, explain why present values are dependent upon interest rates.

Problem 2-6

Find the present values of the following cash flow streams. The appropriate interest rate is 8 percent.

Year Cash Stream A Cash Stream B
1 \$100 \$300
2 \$400 400
3 400 400
4 400 400
5 300 100

Problem 2-10

Find future values of the following ordinary annuities:

a) FV of \$400.00 each 6 months for 5 years at a nominal rate of 12 percent, compounded semiannually.
b) FV of \$200.00 each 3 months for 5 years at a nominal rate of 12 percent compounded quarterly.
c) The annuities described in parts a and b have the same amount of money paid into them during the 5 year period and both earn interest at the same nominal rate, yet the annuity in part b earns \$101.75 more than the one in part A over 5 years. Why does this occur?

Problem 2-11

Universal Bank pays 7 percent interest, compounded annually, on time deposits. Regional bank pays 6 percent interest, compounded quarterly.

a) Based on effective interest rates, in which bank would you prefer to deposit your money?
b) Could your choice of banks be influenced by the fact that you might want to withdraw your funds during the year as opposed to at the end of the year? In answering this question, assume that funds must be left on deposit during the entire compounding period in order for you to receive any interest.

Problem 6-6

The Garraty Company has two bond issues. Both bonds pay \$100.00 annual interest plus \$1,000 at maturity. Bond L has a maturity of 15 years, and bond S a maturity of 1 year.

a) What will be the value of each of these bonds when the going rate of interest is (1) 5 percent, (2) 8 percent, (3) 12 percent? Assume that there is only one more interest payment to be made on bond S.
b) Why does the longer term (15 year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year)?

Problem 6-8

Six years ago, the Singleton Company sold a 20-year bond issue with a 14 percent annual coupon rate and a 9 percent call premium. Today, Singleton called the bonds. The bonds originally were sold at their face value of \$1,000. Compute the realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange for the call price.

Problem 6-9

A 10-year, 12 percent semiannual coupon bond, with a par value of \$1,000, may be called in 4 years at a call price of \$1,060. The bond sells for \$1,100. (Assume that the bond has just been issued).

a) What is the bond's yield to maturity?
b) What is the bond's current yield?
c) What is the bond's capitol gain or loss yield?
d) What is the bond's yield to call

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