# Accrued Interest

Accrued interest is the amount of interest receivable on a bond between the calculation date and last payment date. It equals the product of the bond's face value, its periodic coupon rate and the ratio of days lapsed since last payment date to total days in the payment period.

Bonds pay interest at specific intervals, but they are traded daily. In order to determine the value of a bond between two payment dates, accrued interest must be accounted for. Calculation of accrued interest is also import for financial reporting purpose.

## Formula

Accrued Interest = F × r × TF

Where,
F is Face Value of the Bond
r is the coupon rate for the period and it equals annual coupon rate divided by number of periods in a year

TF stands for time factor and equals days lapsed since the last payment divided by total days in the payment period. It depends on the day count convention of the bond.

## Example

GE has 3 million $1,000 par 2.7% semi-annual coupon bonds maturing on 9 October 2022. The first payment was due on 9 April 2013 and next payment is due on 9 October 2013. Find the accrued interest on a bond as of today, 19 July 2013. The bond uses 30/360 day count convention. Solution  Accrued Interest =$1,000 × 2.7% × 100 = \$7.5 per bond 2 180

Since the bond is a semi-annual bond and it follows 30/360 day count convention, there are 180 days between the two payment dates. Days between last payment date and the calculation date are 100 [21 days of April + 30 days of May + 30 days of June + 19 days of July].

Written by Obaidullah Jan