Bonds might pay interest monthly, quarterly, semiannually, annually or at maturity. Interest accrues, or builds up, between payment dates. If you buy a bond on any date other than a payment date, your purchase price will include accrued interest. In return, you get the full interest amount on the next payment date.
To calculate accrued interest, you'll first choose a day count convention such as 30/360, actual/365 or actual/actual. Then, you'll multiply the day count of the accrual period by the daily interest and the face value.
Day Count Convention
Determine which day count convention the bond uses. The form of a day count convention is a fraction: the numerator is the number of days in the month and the denominator is the number of days in the year. For example, 30/360 means that each month is considered to have 30 days and the year has 360 days. In this convention, you don’t accrue interest on the 31st day of the month. Other common conventions include actual/365 and actual/actual.
Accrued Interest Definitions
For calculating accrued interest on a bond purchase, the “first date” is the most recent payment date and the “second date” is the purchase date. The symbols d1, m1 and y1 denote the day number, month number and year number, respectively, of the first date. For example, a first date of March 21, 2019, has values for d1, m1 and y1 of 21, 3 and 19. Second date symbols are d2, m2 and y2.
Calculating the Accrual Period
To calculate the number of days in the accrual period for a 30/360 convention, you must add together four terms. The first term is the maximum of 0 and (30 minus d1). The second term is the minimum of 30 and d2. The third term is 360 times (y2 minus y1). The fourth term is 30 times (m2 minus m1 minus 1).
Day Count Example
Suppose you buy a $1,000 bond that pays 6 percent annual interest in two semiannual payments of 3 percent each and uses the 30/360 convention. You buy the bond for $960 on February 14, 2019 -- this is the second date. The bond last paid interest on Dec. 1, 2018, which is the first date. To figure the day count in the accrual period, calculate each of the four terms. The results are 29, 14, 360, and minus 330, giving a day count of 73 days.
Calculating Accrued Interest
Calculate the accrued interest by multiplying the day count by the daily interest rate and the face value. In this example, the daily interest rate is 6 percent divided by 360 days, or 0.017 percent per day. The calculation is $1,000 times 0.00017 times 73 days, or $12.17 accrued interest. If you buy the bond for $960, you will have to pay $972.17, plus commission. On June 1, 2019, you’ll receive a semiannual interest payment equal to 3 percent of $1,000, or $30. Your net interest for the period is $30 minus $12.17, or $17.83.
Accrued Interest Considerations
Most U.S. corporate and municipal bonds use the 30/360 convention. This convention has secondary rules. For example, change d2 from 31 to 30 when d1 is 30 or 31. Also, if d1 is 31, change it to 30. Variations on this method might apply end-of-month rules, such as paying monthly interest on the last day of the month. Treasury bonds use the actual/365 day count convention. You can get an actual day count on spreadsheets and business calculators by using the “days” function.