Accrued Interest

What is accrued interest?

Accrued interest is the coupon income from the previous coupon date to the settlement date of the bond.

If a holder decides to sell a bond before it pays the next coupon, the investor will still collect a part of the coupon income for the number of days the bond was owned. This part is called “accrued interest”. Knowing the previous and next coupon date is therefore important in calculating what the accrued interest for that bond will be at any point in its life.

For example, say an investor holds a Eurobond that pays a coupon every 180 days (semi-annually with a 30/360-day convention). So far, the Eurobond is held for 110 days since the previous coupon date. In the event of a sale of the position, the holder will receive the 110/180-day part of the coupon. It is said that the investor “gives up” the remaining 70 days.

180 days110 days70 days180 days

Previous Coupon Date                   Next Coupon Date

Accrued interest is based on the settlement date and not on the trade date. For example, if a bond settles a day after the coupon date, there will be 1 day of accrued interest. Also, when a bond settles on the coupon date, the buyer will not pay any accrued interest and the seller receives all (i.e. the coupon). 

Accrued interest is added to the principal amount to demonstrate the total cash amount of the transaction. Alternatively, or in addition, accrued interest can be quoted as a price component and will be added to the clean price.

What is the difference between a clean and a dirty price?

Bond prices are always in percentages, but we tend to drop the percentage sign in a quote. So, 98.50 is effectively 98.50%. furthermore, Eurobonds are always quoted “clean” of accrued interest. When we add accrued interest to the price, we get the “dirty price”.

How is accrued interest calculated?

In order to calculate the correct amount of accrued interest, a day count adjustment is needed when calculating the difference between the previous coupon date and the settlement date. This adjustment ensures that every month has 30 days and not 31 for example for December or 28 (or 29) for February.

The below schedule uses the 2025 Republic of Nigeria Eurobond once more for illustrative purposes.

For the days between the Settlement Date and the Previous Coupon Date an adjustment is needed to arrive at 145 days. A total of 147 calendar days has passed since the Previous Coupon Date and the Settlement Date, however the months December (31 days), January (31 days), February (29 days) and March (31 days) all need to be adjusted to 30 days. This means an addition of 1 day to February and a subtraction of 1 day for the other months, means a total of minus 2 days.

No day adjustment is needed to calculate the days to the Next Coupon Date as the month of April already counts 30 days.

Once it is clear how many days the bond has been held and adjusted to the day-count convention, a simple formula follows to calculate the accrued interest:

Nominal Amount *Coupon Rate * Days since Previous Coupon