# Formula for Calculating the APY on Bonds

by David Ingram ; Updated April 19, 2017Annual percentage yield (APY) is a calculation investors use to compare bonds with similar debt instruments featuring different interest-compounding schedules. The APY calculation results in a normalized approximation of interest expected to be received in one year, based on an annual compounding period. Investors can calculate APY on bonds using a scientific calculator, although there are a number of free online calculators that can determine APY. It is also used to determine and compare the expected future values of bonds and other debt instruments.

## Bond Interest Rate

The first variable to define for the APY formula is the bond interest rate. Interest rates on bonds vary, creating the need for metrics like APY to compare bonds with different rates. If you purchased a bond from the original issuer, check the original bond indenture or your accounting records for the interest rate. If you are comparing bonds currently on the bond market, check your broker's quotes to find the interest rates. For example, you may wish to compare two bonds on the open market, one offering 10 percent interest and the other yielding 9 percent.

## Number of Compounding Periods

The number of compounding periods is the other variable in the APY formula. The number of compounding periods in one year corresponds to the number of coupon payments made in one year. Most bonds compound semi-annually, including treasury bonds and corporate bonds. However, similar instruments, such as a long-dated Treasury bills, make interest payments more or less frequently than bonds. This requires a metric such as APY to make a reliable comparison. For example, assume you are comparing a bond with a semi-annual compounding period to a similar debt instrument compounding monthly. The bond would have two compounding periods per year, and the other instrument would have 12.

## APY Formula

Use the following formula to calculate the APY on a bond, where N equals the number of compounding periods per year: ( 1 + interest rate / N ) ^ N – 1. If you are comparing a bond and another debt instrument, both yielding 10 percent, with the bond compounding twice per year, and the other option compounding 12 times, the APY on the bond would be .1025 ( 1 + .1 / 2 ) ^ 2 – 1, and the APY on the other option would be .1047 ( 1 + .1 / 12) ^ 12 – 1. Therefore, even though both options yield 10 percent, the second option would yield just barely higher when analyzed to four decimal places.

## Expected Future Value

You can use the APY figure to calculate the expected future value of any bond you hold. Use the following formula to calculate the future value of a bond using the APY: original purchase price x ( 1 + APY) ^ number of years invested

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