# How to Calculate Interest Expense on a Bond Using YTM

by C. Taylor

When you invest in a bond, you are effectively granting a loan to the issuer, such as a corporation or government agency. In exchange for this loan, the issuer agrees to pay periodic interest at a specific rate. When the bond matures, the final coupon payment is made along with the bond's face value. If the purchase price of the bond differs from the face value, the yield-to-maturity rate is used to describe the bond's overall yield to the investor. This YTM rate can be deconstructed to calculate the amount of interest expense the issuer incurs.

1. Add the purchase price of the bond to the face value. Divide this figure by 2 to calculate the average price of the bond. As an example, a \$1,000 bond purchased for \$960 has an average price of \$980.

2. Multiply the average bond price by the yield-to-maturity or YTM rate to determine the effective annual payment. This figure takes into account actual interest payments and amortization of the bond's price difference. If the YTM rate is 9 percent, for example, multiply \$980 by 0.09 to get \$88.20.

3. Subtract the price of the bond from its face value. In the example, \$1,000 minus \$960 is a difference of \$40.

4. Divide the price difference by the bond's maturity term to amortize the difference. If the bond matures in 10 years, divide \$40 by 10 to get \$4.

5. Subtract the amortized price difference from the effective annual payment to get the actual interest payment. Continuing the example, \$88.20 minus \$4 gives an interest payment of \$84.20. This is the interest expense incurred by the issuer each year.

6. Divide the annual interest payment by the bond's face value to calculate the annual interest rate. In the example, \$84.20 divided by \$1,000 yields an interest rate of 0.0842, or 8.42 percent.

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