The Formula for Interest Revenue Accrued on a Bond

by Bryan Keythman

    Although a bond might pay interest only semiannually or at some other interval, the interest revenue, or income, accrues daily. When you buy or sell a bond in between its interest payments, you must account for the interest that has accrued since the last payment. Bond prices quoted in newspapers and financial websites typically do not include this accrued interest amount. You can calculate a bond’s accrued interest to see how much you have to pay on top of the bond’s quoted price if you buy a bond or how much extra you receive if you sell a bond.

    Step 1

    Substitute the bond’s information into the formula C x P x (D/N), in which C represents the annual coupon, or interest, rate, P represents the bond’s par value, D represents the number of days since the last coupon payment and N represents the number of days in the year. Corporate and municipal bonds use a 360-day year to calculate daily interest, while government bonds use a 365-day year. For example, assume a corporate bond with a par value of $1,000 has a 7 percent coupon rate. Assume 30 days have passed since its last coupon payment. The formula is 0.07 x $1,000 x (30/360).

    Step 2

    Divide the numbers in parentheses. In this example, divide 30 by 360 to get 0.0833. This leaves 0.07 x $1,000 x 0.0833.

    Step 3

    Multiply the bond’s annual coupon rate by its par value. In this example, multiply 0.07 by $1,000 to get $70. This leaves $70 x 0.0833.

    Step 4

    Multiply the remaining numbers to calculate the bond’s accrued interest. Concluding the example, multiply $70 by 0.0833 to get $5.83 in accrued interest. This means you receive $5.83 in addition to the bond’s quoted price when you sell the bond.

    Tip

    • A bond’s quoted price plus its accrued interest is called its “dirty” price. For example, a bond with a quoted price of $950 and accrued interest of $5.83 has a dirty price of $955.83.

    About the Author

    Bryan Keythman has performed stock investment research and writing for a consulting firm since 2008. He also has prior experience sourcing and underwriting commercial real-estate investment and development opportunities for a commercial real-estate developer. Keythman holds a Bachelor of Science in finance.

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