# Accrued interest

In finance, accrued interest is the interest on a bond or loan that has accumulated since the principal investment, or since the previous coupon payment if there has been one already.

For a financial instrument such as a bond, interest is calculated and paid in set intervals (for instance annually or semi-annually). Ownership of bonds/loans can be transferred between different investors not just when coupons are paid, but at any time in-between coupons. Accrued interest addresses the problem regarding the ownership of the next coupon if the bond is sold in the period between coupons: Only the current owner can receive the coupon payment, but the investor who sold the bond must be compensated for the period of time for which he or she owned the bond. In other words, the previous owner must be paid the interest that accrued before the sale.

## Formula

The primary formula for calculating the interest accrued in a given period is:

$I_{A}=T\times P\times R$ where $I_{A}$ is the accrued interest, $T$ is the fraction of the year, $P$ is the principal, and $R$ is the annualized interest rate.

$T$ is calculated as follows:

$T={\frac {D_{P}}{D_{Y}}}$ where $D_{P}$ is the number of days in the period, and $D_{Y}$ is the number of days in the year.

The main variables that affect the calculation are the period between interest payments and the day count convention used to determine the fraction of year, and the date rolling convention in use.

A compounding instrument adds the previously accrued interest to the principal each period, applying compound interest.