# How do I Compute Bond Equivalent Yield & the Effective Annual Rate?

Money has time value, and it’s called interest. When you earn interest, you have the opportunity to reinvest it to earn even more interest – that’s called compounding. Effective annual rate is the actual annual rate you earn on debt that compounds more than once a year. Bond equivalent yield is a method of equating the yield on a short-term discount bond -- one that is selling for less than its face value and matures in less than one year -- with that of an annual-coupon bond.

## Computing Effective Annual Rate

First, verify how many times the bond compounds within a year, and divide this into the stated bond interest rate, giving the rate per period. Next, add one to the rate per period and then raise it by an exponent equal to the number of periods per year. Finally, subtract one. Your result is the effective annual rate. You can use this procedure to compare the returns on several different bonds to determine which one has the highest annual rate.

## Example Calculation of Effective Annual Rate

We'll use a monthly fixed income instrument, so that the number of compounding periods is 12. The non-compounded annual rate is always clearly stated in any offering for a fixed-income security. For this example, we’ll assume an annual rate of 10 percent. The rate per period is 0.10 divided by 12, or 0.0083. Adding one gives us 1.0083. When we raise this by the power of 12, we get 1.1047. Subtract one and convert to a percentage to get 10.47 percent as the effective annual rate.

## Computing Bond Equivalent Yield

Face value is the amount of principal returned at maturity. As a point of reference, many bonds carry a $1,000 face value. Determine the percentage return on investment by subtracting the purchase price from the face value and divide the result by the purchase price. The maturity date will be clearly stated in the bond offering -- use this to calculate the days until maturity, and divide the result into 365 to get the time factor. The bond equivalent yield equals the percentage return on investment multiplied by the time factor.

## Example Calculation of Bond Equivalent Yield

If you already own the bond, check your records for price. Otherwise, use the current ask price of the bond, which is listed on the bond exchange. In this example, the purchase price is $975. This gives us a percentage return on investment of $1,000 minus $975, divided by $975, resulting in 2.56 percent. Assuming 100 days until maturity, the time factor is 365 divided by 100, or 3.65. The bond equivalent yield is is 2.56 percent multiplied by 3.65, or 9.36 percent.

References

Resources

- Bond Math: The Theory Behind the Formulas; Donald J. Smith
- The Bond Book, Third Edition: Everything Investors Need to Know About Treasuries, Municipals, GNMAs, Corporates, Zeros, Bond Funds, Money Market Funds, and More; Annette Thau
- Fixed Income Mathematics, 4E: Analytical & Statistical Techniques; Frank J. Fabozzi

Writer Bio

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