# The Formula for Interest Revenue Accrued on a Bond

by Sue-Lynn Carty

When you buy a bond, the interest on it accrues until your scheduled payment date. On that date, the bond issuer pays you the accrued interest amount. The interest revenue accrued on a bond is referred to simply as accrued interest. The formula to calculate the accrued interest is interest rate multiplied by par value, divided by the number of days, divided by 360.

## Formula Definitions

The interest rate is the interest rate payable on the bond. The par value is the face value of the bond. You also need to know the bond’s accrual period. The number of days for new bond issues is the amount of days the between the issue date of the bond, and the day it is delivered to investors. The number of days for existing bond issues is the time between interest payment dates.

## Accrual Period Variations

If your bond has a 30-day accrual period, then the interest accrues every 30 days. For this type of bond, divide the number of days in the equation by 360. If your bond has a calendar month accrual period, then the interest on your bond accrues according to the number of days in each month. For bonds that use calendar dates, such as federal government bonds, divide the number of days in the equation by 365, not 360.

## Example 360 Day Year

Assume that you buy a corporate bond on March 1 and the next interest payment date is July 1, and the accrual period for the bond is every 30 days. Also assume the interest rate is 7 percent, and the par value of the issues is \$100. The only input to the accrued interest formula that is not readily available is the number of days. Interest accrues on your bond every 30 days, the time from your purchase to the time the next interest payment is due is four months, or 120 days. Your accrued interest is then .07 x \$100 (120 / 360) = \$2.33.

## Example 365 Day Year

In this example, assume you buy a Treasury bond April 1, and the next interest payment date is July 1. Treasury bonds use calendar accrual periods. Five percent and the par value of the issues is \$1000, and interest accrues on your bond according to calendar months. So the next interest payment is due 91 days. Your accrued interest is then .05 x \$1000 (91 / 365) = \$12.47.

#### Photo Credits

• Photos.com/Photos.com/Getty Images