For bond holders, interest accumulation is everything. Bond investors rely on coupon payments as a form of fixed income, usually paid twice yearly. And while the interest payment for a fixed-interest bond is the same thing on each payment date, interest accumulation occurs between these dates and the time the bond actually settles. To understand the amount accumulated, bondholders need to observe the day-count convention.

A day-count convention is the method of calculating accrued interest between coupon payment dates for a bond or credit swap. Using this convention, financial institutions can both understand the amount of interest against an upcoming bond payment, as well as document that accumulation through transparent means.

There are several day-count conventions, each designed with the same intent: to provide a real-time interest figure. Here’s a closer look at each of them, and their role in interest accrual transparency.

## The Variables Required to Calculate Accrued Interest

Before we delve into the different day-count convention methods, it’s important to understand the information that goes into calculating interest accrual. In any convention, the variables are the same:

• The principal of the bond is necessary to understand the coupon payment in dollars.
• The interest rate of the bond is necessary to understand the rate of return on the bond.
• Payment dates are the dates the bond pays out its coupon payments to holders.
• Settle date is the date the bond payment actually settles between payment dates.

All of these variables are important for understanding the amount of interest accrued by the bond at the time of its settlement. Below, we’ll detail the three most common methods for calculating it: 30/365, 30/360 and actual/actual.

For each of the examples below, assume a \$1,000 bond with a 6% interest rate that pays out biannually (\$30 payment twice per year) on March 1 and September 1. The settle date is June 3.

## The 30/365 Day-Count Convention

This method calculates daily interest using a 365-day year, then multiplies that by 30 to represent a standardized month. It’s designed to account for every single day of the year. To calculate interest using this day-count convention, institutions would observe the following:

• Calculate the number of days between the payment date and the settle date, assuming 365 days in a year. In this example, there are 124 days between March 1 and June 3.
• Find the percentage of days elapsed against the total days in the period, assuming 30-day months. In this example, there are 180 days between March 1 and September 1, which means the settle date represents 68.88% of the period.
• Multiply the percentage of days elapsed by the amount of an individual coupon payment to get total accumulated interest. In this example, 68.88% of a \$30 payment is \$20.66.

Lots of interest rate swaps use this method of calculating accrued interest, as it tends to account for the concept of lock-in interest rates over the span of a fiscal year (365 days).

## The 30/360 Day-Count Convention

This method assumes that there are 360 days in the year, and that each month is 30 days long. This effectively rounds the numerator (total days in the period) to an even number, which makes it easier to compute interest. Using this method:

• Figure out the number of days between the payment date and the settle date, assuming 360 days in a year. In this example, there are 122 days between March 1 and June 3.
• Find the percentage of days elapsed against the total days in the period, assuming 30-day months. In this example, there are 180 days between March 1 and September 1, which means the settle date represents 67.78% of the period.
• Multiply the percentage of days elapsed by the amount of an individual coupon payment to get total accumulated interest. In this case, 67.78% of a \$30 payment is \$20.33.

Most fixed-rate bonds use the 30/360 method, since it’s a way to account for the full year in a highly standardized way.

## The Actual/Actual Day-Count Convention

This method accounts for the varying length of each month and the actual length of the year. As a result, it provides a more accurate depiction of accrual with regard to the bond’s specific payment and settle dates. Here’s a look at how to calculate it:

• Figure out the number of days between the payment date and the settle date. In this example, there are 124 days between March 1 and June 3.
• Find the percentage of days elapsed against the total days in the period. In this example, there are 184 days between March 1 and September 1, which means the settle date represents 67.39% of the period.
• Multiply the percentage of days elapsed by the amount of an individual coupon payment to get total accumulated interest. In this case, 67.39% of a \$30 payment is \$20.21.

All U.S. Treasuries use the actual/actual standard, since all days in a period carry equal accumulation value.

## Other Day-Count Conventions to Consider

In addition to the three primary modes outlined above, there are also actual/360 and actual/365 methods. These represent the actual days elapsed between a coupon pay date and the settle date, while standardizing the year. This can be helpful for calculating very specific interest accumulation against a recognized standard (year).

Note that the day-count convention used varies across different financial institutions, as well as across different bond types. What matters is that the method stays the same throughout the life of the bond.

## Why is Day-Count Convention Important?

However it’s applied, a day-count convention is critical for understanding interest accumulation at a granular level. Not only can investors better-understand the value of their bonds at any given point between coupon payouts, financial institutions have a way of reporting that accumulation against a standardized metric. Just keep in mind the mode when looking at total accrued interest figures.