# How to Calculate the Effective Interest Rate for Discounted Bonds

After purchasing a bond, you receive regular coupon payments until the bond matures, at which time you receive the face value of the bond along with the final coupon payment. Discounted bonds are those purchased below their face values. The difference between your purchase price and the final face value payment adds to your profit, which means your effective interest rate is higher than the originally stated amount. Although you can calculate the effective interest rate through lengthy calculations, you can get a very close estimate by using a simple formula.

Subtract bond's purchase price from its face value. As an example, if you purchased a \$1,000 bond for \$950, subtract \$950 from \$1,000 to get \$50.

Divide this figure by the number of coupon payments made throughout the bond's life. If the example bond paid twice per year for 10 years, you would divide \$50 by 20 to get \$2.50.

Add the amount of a single coupon payment to the result. If the example bond made periodic coupon payments of \$50, add \$50 to \$2.50 to get \$52.50. If you only know the coupon rate, divide the coupon rate in decimal format by the number of periods in a year. Multiply this figure by the bond's face value. In the example, if the bond offered a 10 percent coupon rate, divide 0.10 by 2 to get 0.05. Multiply \$1,000 by 0.05 to calculate coupon payments of \$50 each.

Add the bond's purchase price and face value, and then divide by 2. In the example, \$1,000 plus \$950 gives you \$1,950. Dividing by 2 gives you \$975.

Divide the figure from Step 3 by the figure in Step 4. In the example, \$52.50 divided by \$975 gives you a periodic effective interest rate of 0.0538.

Multiply this rate by the number of periods in a year to calculate the effective annual interest rate. In the example, there are only two payment periods per year, so multiply 0.0538 by 2 to get an effective annual interest rate of 0.1076, or 10.76 percent.

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