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# Future and Present Values-Annuities

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Use the following information in answering Cases 1 and 2 below:

On January 1, 1998, Dodd Company sold \$800,000 of 10% bonds, due January 1, 2008. Interest on these bonds is paid on July 1 and January 1 each year. According to the terms of the bond contract, Dodd must establish a sinking fund for the retirement of the bond principal starting no later than January 1, 2006. Since Dodd was in a tight cash position during the years 1998 through 2003, the first contribution into the fund was made on January 1, 2004.

Case 1: Assume that, starting with the January 1, 2004 contribution, Dodd desires to make a total of four equal annual contributions into this fund. Compute the amount of each of these contributions assuming the interest rate is 8% compounded annually.

Case 2: Assume, instead, that starting with the January 1, 2006 contribution, Dodd desires to make a total of five equal semiannual contributions into this fund. Compute the amount of each of these contributions assuming the annual interest rate is 12%, compounded semiannually.

Case 3: On January 2, 2004, Notson Company loaned \$50,000 to Pine Company. The terms of this loan agreement stipulate that Pine is to make 5 equal annual payments to Notson at 10% interest compounded annually. Assume the payments are to begin on December 31, 2004. Compute the amount of each of these payments.

In computing your answers to the cases below, you can round your answer to the nearest dollar. Present value tables are provided on the next page.
(see charts in the attached file)

#### Solution Summary

The solution calculates the value of annuities for annual and semi annual compounding.

\$2.19

## Bond prices and interest rates: the relationship

Discuss the relationship between interest rates and bond prices? When must the yield to maturity of a bond equal the current yield? What makes some bonds sell at a premium while others sell at a discount?

Discuss how to use the tables to determine Present and Future Values, or Present Value and Future Annuities.

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