# How to Convert Interest Rates to Discount Rates

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Some bonds don't pay interest directly to investors. Two examples are paper U.S. Series EE savings bonds the Treasury Department sold prior to 2012, and zero-coupon bonds sold by governments and corporations. Issuers sell these bonds at a discount off the face value, and interest accrues. Bond issuers calculate the discount rate using the bond's annual interest rate and the maturity date.

With conventional bonds, the bond issuer sends you fixed interest payments, usually at six month intervals. When bonds such as zero-coupon bonds are sold at a discount, the bond issuer adds interest to the bonds, increasing their value. These bonds therefore pay compound interest, because the amount of interest earned increases as the value of the bond grows. The bond issuer calculates a discount price, or rate, such that accrued interest increases the value of the bond to exactly face value when the bond matures.

Compute the periodic interest rate. A periodic rate is the portion of the annual interest that is added at regular intervals. Bonds typically pay interest twice a year, so the periodic rate equals half of the annual rate. For example, if the annual rate is 6 percent, the periodic rate is 3 percent.

Calculate the total number of interest payments over the life of the bond. If the bond matures in 10 years and pays interest twice a year, multiply 2 times 10. In this example, there are 20 payments.

Compute the appreciation ratio of the bond over its lifetime. The formula is:

A = (1 + P)n

where A equals the appreciation ratio, P is the periodic rate and n is the number of payments. With a 6 percent annual interest rate for a 10-year bond and interest paid twice a year, you have A = (1 + .03)20. The appreciation ratio A works out to 1.80611. In other words, at maturity, the bond will be worth 1.80611 times its original discounted price.

Divide the face value of the bond by the appreciation ratio to calculate the discounted value. Suppose the zero-coupon bond in step 3 has a face value of \$1,000. Divide \$1,000 by 1.80611 to convert to the discounted value of \$553.68. This is the price the bond issuer sets so the bond will be worth exactly \$1,000 at maturity.