# Accrued Interest

## Definition

The term accrued interest refers to the funds that are payable but not yet received because of a timing difference of cash flows.  Accrued interest is oftentimes use in the context of a bond or another type of fixed income security.

### Calculation

Accrued Interest = Fraction of Year x Principal x Rate of Interest

Where:

• Fraction of Year is equal to the number of days in the period divided by the number of days in a year.
• Principal is the remaining balance on the fixed income security or bond.
• Rate of Interest is an annualized interest rate payable on the bond or security.

### Explanation

Bonds make interest payments to bondholders at fixed intervals throughout the year, but the ownership of the bond can be transferred to another party at any time.  The concept of accrued interest allows holders of fixed income securities, such as bonds, to be made whole for funds that are payable but not yet received if they decide to sell the security.  Only the holder of the bond is eligible to receive the coupon payment.  This means the market value of a bond is not just a function of interest rates and time to maturity, but also the value of the accrued interest.

Accrued interest can also refer to the interest earned on an outstanding receivable but not yet paid.  For example, a company may sell goods to a customer and charge a rate of interest equal to 1% of the outstanding balance on the account if payment is not received in 30 days.

### Example

Ann is thinking about selling \$10,000 of Company A's bonds with a coupon rate of 5.000%.  She knows the market value of the bonds, but would like to understand how much of that value is a function of the bond's accrued interest.  The bond makes coupon payments quarterly, and it has been 63 days since the last payment.  The calculation of accrued interest would be:

= (63 days / 365 days) x \$10,000 x 5.000%
= 0.1726 x \$10,000 x 0.005, or \$86.30