Accrued interest is calculated by multiplying the current principal balance by the annual interest rate, dividing by the number of days the contract treats as a year, and then multiplying by the number of days that have passed since the last payment. That last piece — the “days in a year” figure — isn’t always 365. Depending on the instrument, it may be 360, 365, or the actual calendar length, and the choice can meaningfully change what you owe.
The Formula and Its Inputs
Every accrued interest calculation, whether on a mortgage, a commercial loan, or a bond, follows the same equation:
Accrued Interest = Principal × (Annual Rate ÷ Days in Year) × Days Elapsed
Three inputs drive it. The principal is the current unpaid balance on a loan or the face value of a bond, typically $1,000 per bond. On an amortizing loan, use the balance from your most recent statement, not the original loan amount. The annual rate is the nominal rate stated in the loan agreement, promissory note, or bond indenture, converted from a percentage to a decimal (6% becomes 0.06). The elapsed days run from the date of the last interest payment through the date you’re measuring, whether that’s a payoff date, a closing date, or a bond settlement date.
The denominator is set by the contract, and it’s the piece most borrowers overlook.
Day-Count Conventions
A day-count convention is the rule a contract uses to measure time for interest purposes. It tells you both how to count the days that have passed and what number to divide the annual rate by. Different instruments follow different conventions, and applying the wrong one gives the wrong answer even when everything else is right.
30/360 (Bond Basis)
This convention treats every month as 30 days and every year as 360 days, regardless of the calendar. February has 30 days. So does December. The simplification made manual calculation easier, and it became standard for corporate bonds, municipal bonds, and many agency bonds in the United States. Under 30/360, the period from March 15 to April 15 is exactly 30 days, even though the calendar shows 31.
Actual/360
Commercial loans and money-market instruments frequently use Actual/360. You count the real calendar days, but you still divide the annual rate by 360 to get the daily factor. That combination raises the effective annual cost above the stated rate. Because a slightly larger daily rate gets applied across 365 real days, a 6% loan under Actual/360 works out to roughly 6.08% per year. Borrowers who don’t check the day-count clause in their loan agreement often miss this.
Actual/Actual and Actual/365
U.S. Treasury securities calculate yields based on actual day counts on a 365- or 366-day year basis, not 30/360.1U.S. Department of the Treasury. Interest Rates – Frequently Asked Questions Actual/Actual is the most precise method because it recognizes leap years and the true length of each month. If an accrual period spans both a regular year and a leap year, the days in each portion divide by 365 and 366 respectively.
Actual/365 (fixed) is a simpler cousin that always divides by 365, even in a leap year. The difference between the two only surfaces when a leap year is in play, and on most individual balances the effect is small. The convention is a fixed term of the instrument, set at issuance or origination, and it does not change over the life of the loan or bond.
Computing the Daily Rate
The daily rate is just the annual rate divided by the convention’s denominator. For a 6% annual rate:
- 360-day convention: 0.06 ÷ 360 = 0.00016667 per day
- 365-day convention: 0.06 ÷ 365 = 0.00016438 per day
The gap looks tiny. But applied to a $500,000 commercial loan across a year, the 360-day convention costs roughly $4,167 more than the 365-day version. Getting the denominator right is the single most important step in the calculation.
A Worked Example
Take a $250,000 loan at 5.5% annual interest under Actual/360, with 45 days since the last payment.
- Daily rate: 0.055 ÷ 360 = 0.00015278
- Daily dollar accrual: $250,000 × 0.00015278 = $38.19
- Total accrued interest: $38.19 × 45 = $1,718.75
If the same loan used Actual/365, the daily rate falls to 0.00015068 and the 45-day total is $1,695.21, about $23.50 less. On a payoff statement, that difference is real money, and it comes entirely from the denominator.
Simple Accrual vs. Daily Compounding
The formula above assumes simple interest, where each day’s accrual is based only on the outstanding principal. Most mortgages and many commercial loans work this way. Yesterday’s unpaid interest does not generate its own interest today.
Credit cards work differently. Most issuers compound daily: each day’s accrued interest is added to the balance before the next day’s interest is calculated. The daily periodic rate is the APR divided by 365, applied to the prior day’s balance plus its accumulated interest. Compounding produces a slightly larger total than simple accrual on the same balance at the same rate, and the gap widens as the balance and the period grow.
Your loan agreement or cardholder agreement tells you which method applies. Language like “daily balance method” or “average daily balance including compounding” points to compound accrual. “Simple interest” or interest calculated only on the principal means no compounding.
Accrued Interest on a Bond Purchase
When you buy a bond between coupon dates, you owe the seller the interest that has piled up since the last coupon. The seller held the bond through that period and is entitled to be paid for it, even though the next full coupon will come to you. The amount you actually pay is the quoted market price (the “clean price”) plus accrued interest, together called the “dirty price.”
The calculation uses the same formula: face value times the coupon rate divided by the day-count denominator, times the days since the last coupon. A $1,000 bond with a 4% coupon on a 30/360 basis, bought 60 days into the coupon period, carries $6.67 in accrued interest (1,000 × 0.04 ÷ 360 × 60).
The accrued interest you pay the seller is not income to you. When the next coupon lands, part of it is simply refunding what you already paid, and the IRS treats that portion as a return of your capital rather than taxable interest.2Internal Revenue Service. Publication 550 (2025), Investment Income and Expenses Your Form 1099-INT will still show the full coupon. To avoid being taxed on your own money, report the full amount on Schedule B, then subtract the accrued interest paid to the seller on a separate line labeled “Accrued Interest,” so only the net flows to taxable income.3Internal Revenue Service. Instructions for Schedule B (Form 1040)
Per Diem Interest at Mortgage Closing
One of the most visible places accrued interest shows up is the closing table. Mortgage interest accrues daily and is paid in arrears, so the first monthly payment does not cover the days between closing and the end of that month. You pay that gap upfront as “prepaid interest” or “per diem interest.”
The math: divide the annual rate by 365, multiply by the loan amount, and multiply by the days from closing through month-end. On a $400,000 loan at 6.5% closing March 10, per diem interest runs for 21 days (March 10 through March 31). The daily rate is 0.065 ÷ 365 = 0.000178, and the daily charge is $71.23. Over 21 days, that’s $1,495.89 due at closing.
Federal regulations require your lender to show this figure on the Closing Disclosure under “Prepaids.”4Consumer Financial Protection Bureau. 12 CFR 1026.38 – Content of Disclosures for Certain Mortgage Transactions (Closing Disclosure) Closing earlier in the month means more per diem days and a bigger charge; closing near month-end shrinks it.
Where the Calculation Goes Wrong
The most common mistake is using the wrong denominator. Assuming a 365-day year on a commercial loan that specifies Actual/360 will understate the interest by about 1.4% per year. On a $1 million balance, that’s roughly $840 a month unaccounted for. Check the day-count clause in the loan agreement before running the numbers.
The second is miscounting days. Does the accrual period include the first day, the last day, or both? Conventions differ, and one day on a $500,000 balance at 7% shifts the total by about $96 under a 365-day count. Payoff statements should specify a “good through” date so there’s no ambiguity.
The third is using a stale principal figure. On amortizing loans, the balance changes with every payment. Pull the current principal from your most recent statement or an amortization schedule. Using the original loan amount overstates the interest.
If You Think the Charge Is Wrong
If a statement shows an interest charge that doesn’t match your own calculation, the Fair Credit Billing Act gives you a formal way to challenge it on open-end accounts. Send a written notice to the creditor’s billing inquiry address (not the payment address) within 60 days of the statement date, including your name, account number, the amount you believe is wrong, and why.5Office of the Law Revision Counsel. 15 USC 1666 – Correction of Billing Errors
The creditor has 30 days to acknowledge the dispute in writing and up to two billing cycles (no more than 90 days) to either correct the error and refund related finance charges or explain why the charge stands. While the investigation is open, you can withhold payment on the disputed amount without being reported delinquent, though you still owe any undisputed portion. Certified mail with a return receipt is worth the small cost — it settles any later argument about whether and when the creditor received your notice.