# The Formula for Interest Revenue Accrued on a Bond

By: Ryan Cockerham | Reviewed by: Ashley Donohoe, MBA | Updated June 11, 2019

When an individual invests in bonds, they do so with the understanding that this particular asset will likely only pay out interest around two to three times a year. That being said, this does not mean that interest is not accruing on this bond on a daily basis. When an investor decides to sell a bond between payout periods, they will need to account for this accrued interest as they calculate a sale price. Fortunately, determining the amount of revenue that has accrued on a bond between payout periods can be accomplished relatively easily.

### Tip

You can easily begin calculating accrued interest on a bond using a simple mathematical formula. That being said, you will need to know the coupon value of the bond, as well as its par value and the number of days since an interest payout has occurred.

## The Basics of Bond Payouts

When an investor chooses to purchase bonds, they do so with the knowledge that these particular investments often provide a safe, reliable way to generate consistent profits at the expense of regular payouts. Unlike standard stocks, bonds feature a concretely defined maturity date at which the full profit of the asset will be realized. Until this maturity date is reached, the bond will generate interest that is paid back to the investor at pre-determined intervals.

Typically, these intervals occur semi-annually, or even only twice a year. Although investors who have put their money into a bond fund, exchange-traded fund or closed-end fund may see payouts more frequently, those who have purchased bonds directly from the market will experience a much slower trajectory.

A unique situation arises when an investor seeks to buy or sell a bond prior to its full maturation. At this point, it is essential that the owner of the bond calculates the amount of interest that has accrued on the bond in order to assess its real value. Under these circumstances, the current value of the bond would likely be noticeably higher than its original purchase price.

## Bond Payout Calculator Formulas

In order to determine the amount of interest that has accrued, a relatively simple mathematical formula can be used – no bond interest calculator necessary.

The correct formula to use is I = C x P x (D/N), where I equals accrued interest, C equals the annual interest rate, P equals the fixed par value of the bond, D is equivalent to the number of days since the last interest payout and N is the number of days in the year, With this formula in mind, consider the following example:

A government bond has a 5 percent coupon rate (interest rate), a par value of \$900 and has not paid out interest in 37 days. With this information, the formula for calculating accrued interest would be:

I = 0.05 x 900 x (37 / 365) = \$4.56

Therefore, if the bond was sold today, its selling price would be the par value plus an additional \$4.56 in accrued interest.

## Important Details for Interest Revenue

It is important to note that government and corporate/municipal bonds use a different value for N in the formula. Whereas government bonds operate on a 365-day year, corporate and municipal bonds use a 360-day year for their interest cycle. Failure to use the right value in the formula could cause minor inconsistencies in your results and introduce flaws into your sale price.

### Tip

• A bond’s quoted price plus its accrued interest is called its “dirty” price. For example, a bond with a quoted price of \$950 and accrued interest of \$5.83 has a dirty price of \$955.83.