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In finance, accrued interest is the interest that has accumulated since the principal investment, or since the previous interest payment if there has been one already. For a financial instrument such as a mortgage, interest is calculated and paid in set intervals but is most commonly accrued daily

Formula

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

I_A = T x P x R

where IA 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 = DP/DY

where DP is the number of days in the period, and DY is the number of days in the year.

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

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..