# What is accrued interest? How to calculate accrued interest

In finance, accrued interest refers to the interest that has accumulated since the principal investment of a bond. The term has the same meaning when talking about loans.

The seller of bonds constructs and pays the interest in predetermined installments. Typically, they pay interest quarterly or annually.

We can transfer a bond or loan at any point in time, and not just after receiving coupon payments. In the world of bonds, the term coupon refers to the interest payments, which usually occur twice a year.

The current owners of financial instruments receive the coupon payments. The previous owners, on the other hand, only receive money for the period that they held them. The ‘previous owners’ are the ones who sold the financial instruments to the current owners.

Hence, this means that the financial instruments’ previous owners receive the interest payment that had accrued before the sale.

## Calculating accrued interest

According to the Municipal Securities Rulemaking Board, the formula for calculating accrued interest on a 360-day year is:

Accrued Interest = (Interest Rate)*(Par Value)*(Number of Days / 360)

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

IA = T x P x R

Where IA Is the accrued interest, T is the fraction of the year, P is the principal, and R equals the annualized interest rate.

To calculate T, we typically use the following formula:

T = DP/DY

DP = The number of days in the set period.
DY = The number of days in the year.

## Examples of accrued interest

Assume that on July 21 a city sold a \$5,000,000 new issue of municipal bonds. The issue and settlement dates on the bonds were May 1 and November 15 respectively. The interest rate on the bonds was 3.5 percent.

Interest amount issuer pays on settlement date = (.035) * (\$5,000,000) * (198/360) = \$96,250