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.

Accrued interest on bonds
Issuers commonly sell bonds on dates other than when they pay the coupons (interest).

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.

Accrued Interest Calculator

Why 360 vs. 365? In finance, day count conventions vary. Some markets use a 360-day year (12 months × 30 days) to simplify calculations, often called the “banker’s year.” Others use a 365-day year to more closely match the calendar. Always check which convention your financial instrument uses.

Examples of accrued interest

Example 1: Municipal Bonds

Assume that on July 21 a city sold a $5,000,000 new issue of municipal bonds. The issue date was May 1, and the settlement date was November 15. The bonds carry an annual interest rate of 3.5%.

Since the period from May 1 to November 15 is 198 days (based on a 360-day year), the interest the issuer must pay on the settlement date is calculated as: 

Interest = (0.035) * ($5,000,000) * (198 / 360) = $96,250

Example 2: Corporate Bonds

Consider a corporate bond with a face value of $1,000 and a 4% annual coupon rate. Coupons are paid semiannually on June 30 and December 31. If an investor purchases the bond on March 31, the number of days accrued since the last coupon payment (December 31) is 90 (assuming a 360-day year).

Therefore, the accrued interest would be: 

Accrued Interest = 0.04 * $1,000 * (90 / 360) = $10.00

Example 3: Personal Loan

Suppose you take out a personal loan of $10,000 at a 6% annual interest rate. Interest is accrued daily based on a 365-day year. You make your first payment after 45 days.

The accrued interest up to that day is: 

Accrued Interest = 0.06 * $10,000 * (45 / 365) ≈ $73.97