Accrued Interest Explained
Accrued Interest Explained
When you buy a bond after it has accrued interest but before the next coupon payment, you pay the seller for the interest they've earned. This accrued interest is separate from the bond's quoted price.
Key takeaways
- Bonds accrue interest daily, even though coupon payments are made only semi-annually (or quarterly, or annually).
- If you buy a bond mid-coupon period, you pay the seller for the accrued interest up to that point.
- Accrued interest is calculated on a day-count basis (Actual/Actual, 30/360, or similar) depending on the bond type.
- The quoted price you see (the clean price) does not include accrued interest; the actual invoice price (dirty price) does.
- Accrued interest resets to zero on each coupon payment date.
Why accrued interest exists
Imagine a corporate bond paying a 4% annual coupon semi-annually (2% every six months). If the bond pays $20 per $1,000 face value on June 15 and December 15, what happens to the bondholder who owns the bond on June 10?
Under the law of contracts, that bondholder has earned five days' worth of coupon interest because they held the bond for five days. If they sell the bond on June 10, the new buyer will receive the full $20 coupon on June 15—but the seller deserved to be paid for those five days of accrued interest.
Without a mechanism to account for accrued interest, the seller would lose money and the buyer would gain a windfall. Accrued interest solves this: the buyer reimburses the seller for the portion of the coupon the seller earned through the sale date.
How accrued interest is calculated
Accrued interest is calculated based on the number of days elapsed since the last coupon payment (or the bond's issue date, if no coupon has been paid yet). The exact calculation depends on the day-count convention used by the bond.
For a bond using the Actual/Actual day-count (common for Treasuries), the calculation is:
Accrued Interest = (Coupon per Period) × (Days Elapsed / Days in Period)
Suppose a Treasury bond pays 3.5% annually (1.75% semi-annually, or $17.50 per $1,000 face value). If 91 days have elapsed since the last coupon payment, and the coupon period is 184 days:
Accrued Interest = $17.50 × (91 / 184) = $17.50 × 0.4946 = $8.66 per $1,000 face value
Corporate bonds often use the 30/360 day-count convention, which assumes each month has 30 days and each year has 360 days. This simplifies calculations and was standard before computers but now persists by convention. The result is often slightly different from Actual/Actual.
Municipal bonds frequently use Actual/Actual as well, though conventions vary by state.
Clean price vs. dirty price (preview)
The price a dealer quotes you—the price you see on a Bloomberg terminal or your brokerage platform—is the "clean price." It does not include accrued interest. A Treasury bond might be quoted at 101.50, meaning 101.5% of par, or $1,015 per $1,000 face value.
The price you actually pay—the invoice price—is the "dirty price," which includes accrued interest. If accrued interest is $8.66 per $1,000, your invoice price is 101.50 + 0.866 = 102.366, or $1,023.66 per $1,000 face value.
The reason for separating clean and dirty price is to stabilize the quoted price around coupon payment dates. The dirty price would swing significantly around coupon dates (jumping up as accrued interest accumulates, then dropping when the coupon is paid). The clean price is more stable, making it easier to track and compare bonds over time.
The timeline of accrued interest
Consider a bond paying coupons on March 15 and September 15. If you buy the bond on June 15 (exactly three months into the coupon period), accrued interest accumulates for three months out of six. On September 14 (one day before the coupon), accrued interest has accumulated for nearly six months.
On September 15, when the coupon is paid, accrued interest resets to zero. The new owner of the bond (who bought it on September 14) receives the full coupon payment on September 15, even though they held it for only one day. They then owe the previous owner for the accrued interest on that day.
This might seem odd, but it works because accrued interest and coupon payments interact. The new owner pays the previous owner for accrued interest, so the economic transfer is correct.
Example: buying a bond between coupon dates
Say you buy $100,000 face value of a corporate bond at a clean price of 102.00 (meaning 102% of par). The bond pays 4% annually, with coupons on February 1 and August 1. You buy it on April 1—exactly 59 days into the 181-day coupon period.
The semi-annual coupon is $2,000 ($100,000 × 0.04 ÷ 2).
Accrued interest = $2,000 × (59 / 181) = $2,000 × 0.3260 = $652
Your invoice price is:
- Clean price: $102,000
- Accrued interest: $652
- Total invoice price: $102,652
You pay $102,652 for the bond. On August 1, you receive a $2,000 coupon payment. Because you held the bond for 122 days out of the 181-day period (from April 1 to August 1), you've earned $2,000 × (122 / 181) = $1,348 of that coupon. The $652 you paid upfront compensates the previous owner for their portion.
Accrued interest and taxes
From a tax perspective, accrued interest is taxable income in the year it is received. If you buy a bond between coupon dates and receive a coupon payment three months later, the coupon is taxable. The accrued interest you paid to the previous owner is added to your cost basis, not deducted from income.
This is why many investors prefer to hold bonds in tax-advantaged accounts (401(k), Roth IRA, traditional IRA) where accrued interest and coupon income don't trigger annual tax bills. In taxable accounts, you'll owe income tax on coupon payments every year, even if you don't spend the money.
The settlement convention
Bond trades typically settle on a "T+1" basis (trade date plus one business day) or sometimes "T+2" (trade date plus two business days). This delay means accrued interest is calculated for the settlement date, not the trade date. You and the dealer agree on a price and accrued interest based on settlement, which is usually one or two business days in the future.
During this brief settlement window, accrued interest can change if a coupon payment date intervenes. This is rare for short settlement periods but possible, especially for bonds with unusual coupon schedules.
Why accrued interest matters for your planning
Accrued interest increases the true cost of buying a bond. A clean price of 102 might be attractive until you realize accrued interest adds another 0.5 to 2 percentage points, depending on where you are in the coupon cycle.
For buy-and-hold investors, this doesn't matter much; you'll receive that interest as coupon payments over time. But for traders or market timers, accrued interest is a real cost that affects returns.
Additionally, if you're reinvesting coupon payments, accrued interest and coupons together make up your total cash return. Understanding this helps you forecast your actual income from bond holdings.
How accrued interest flows through settlement
Related concepts
Next
We've seen that the true price you pay for a bond includes accrued interest. The distinction between the clean and dirty price is one of the most practical pricing concepts you'll encounter. Let's explore how these two prices work together and why the bond market separates them.