To calculate accrued interest, multiply the principal balance by the annual interest rate (written as a decimal) and then by the fraction of the year that has passed since the last payment or credit. That single formula handles most simple-interest situations. Compound products, variable-rate loans, and bonds add wrinkles, but the arithmetic still starts from those three inputs: principal, rate, and time.
The Three Inputs You Need
The principal is the outstanding balance of a loan or the face value of an investment. For a loan, your most recent statement or online account shows the current balance. For a bond or certificate of deposit, the principal is the amount you originally invested or the bond’s par value.
The annual interest rate appears in your loan’s Truth in Lending disclosure.1eCFR. 12 CFR Part 1026 – Truth in Lending (Regulation Z) Convert the percentage to a decimal by dividing by 100, so 5% becomes 0.05. The time period is the window you’re measuring, expressed as a fraction of a year. For 90 days of accrued interest, the time factor is 90 divided by 365 (or 360, depending on the contract’s day count convention).
If Your Rate Is Variable
A variable rate is built from a benchmark index plus a fixed margin. Most variable-rate consumer and commercial loans in the United States now use the Secured Overnight Financing Rate (SOFR) as their benchmark.2New York Fed (Alternative Reference Rates Committee). An Updated Users Guide to SOFR If SOFR is 3.70% and your margin is 2.00%, your current rate is 5.70%. Check your loan agreement for the margin and the reset schedule, then use the current combined rate.
The Simple Interest Formula
Simple interest is the standard method for short-term loans, auto loans, mortgages, and certificates of deposit. The formula is:
Interest = Principal × Rate × Time
Suppose you owe $10,000 at 6% annual interest and want to know how much interest accrues over 90 days. Multiply $10,000 by 0.06 to get $600 in annual interest. Then multiply $600 by 90/365, which gives roughly $147.95. If your contract uses a 360-day year instead, the same calculation yields $150.00, because the smaller denominator produces a slightly higher daily rate.
Per Diem Interest on a Mortgage Payoff
Mortgage interest accrues daily on the remaining balance. Each month, the lender multiplies the outstanding principal by your monthly rate (annual rate ÷ 12). Your fixed payment covers that interest first, and whatever is left reduces principal. Early in a 30-year loan, almost all of your payment goes to interest; by the end, almost all of it goes to principal.
On a $200,000 mortgage at 5%, the monthly rate is about 0.4167%. The first month’s interest is $200,000 × 0.004167 = $833.40. If your fixed monthly payment is $1,073.64, only $240.24 reduces the balance that month. The next month’s interest starts from $199,759.76.
This daily accrual matters most when you pay a loan off. Interest keeps accumulating between your last payment and the payoff date, so your final amount due includes per diem interest for those extra days. Divide your annual interest by 365 and multiply by the number of days since your last payment. On a $200,000 balance at 5%, per diem interest runs about $27.40 a day. Closing on a Wednesday instead of a Monday costs an extra $54.80.
The Compound Interest Formula
Compound interest is calculated on both the original principal and all previously accrued interest. Savings accounts, credit cards, and most long-term investment products compound in some form. The formula is:
A = P × (1 + r/n)n×t
- A is the total future value (principal plus accrued interest)
- P is the original principal
- r is the annual interest rate as a decimal
- n is the number of times interest compounds per year
- t is the number of years
To isolate just the interest, subtract the original principal: Interest = A − P.
Say you deposit $5,000 at 4% compounded monthly for two years. Then n = 12 and t = 2, so the exponent is 24. Inside the parentheses: 1 + (0.04/12) = 1.003333. Raise that to the 24th power to get about 1.08314. Multiply by $5,000, which comes to $5,415.70. Subtract the original $5,000, and accrued interest over two years is about $415.70. Compounding monthly instead of annually adds roughly $3.50 in this example, but that gap widens with larger balances and longer horizons.
Credit Card Interest
Credit cards use compound interest through the average daily balance method.3Consumer Financial Protection Bureau. How Does My Credit Card Company Calculate the Amount of Interest I Owe The issuer tracks your balance each day of the billing cycle, adds those daily balances together, and divides by the number of days in the cycle. It then multiplies that average by the daily periodic rate (APR ÷ 365).
If you pay your full statement balance by the due date, most cards charge no interest on new purchases. Carry any balance past the due date and you lose the grace period. Interest then accrues on the unpaid amount and on every new purchase from the date of the transaction itself, not from the end of the billing cycle.4Consumer Financial Protection Bureau. What Is a Grace Period for a Credit Card Because interest compounds daily, paying down part of your balance mid-cycle reduces the average daily balance for every remaining day.
Day Count Conventions Change the Answer
The denominator you use when converting an annual rate to a daily rate isn’t always 365. Financial contracts specify a day count convention, and using the wrong one throws off the result. Three conventions cover most situations:
- 30/360. Assumes every month has 30 days and the year has 360. Standard for U.S. corporate and municipal bonds. Slightly overstates daily interest compared to actual calendar days.
- Actual/365. Uses the real number of days in the accrual period divided by 365. Common for consumer products like auto loans and personal credit lines.
- Actual/Actual. Uses the real number of days in both the numerator and denominator, with 366 in a leap year. U.S. Treasury bonds use this method.
The difference sounds academic until you run the numbers. On a $500,000 commercial loan at 6%, the 30/360 convention produces $83.33 of daily interest ($500,000 × 0.06 ÷ 360), while Actual/365 produces $82.19 ($500,000 × 0.06 ÷ 365). Over 90 days, that’s a gap of about $102. If your calculations don’t match a statement or a payoff quote, the day count convention is the first thing to check.
Buying a Bond Between Coupon Dates
When you buy a bond between scheduled interest payment dates, you pay the seller for the interest that built up while they owned it, and that accrued interest is added to your purchase price. When the next coupon arrives, you receive the full payment for the entire period even though you only held the bond for part of it. The accrued interest you paid the seller reimburses them for their share.
To calculate accrued interest on a bond purchase, multiply the face value by the coupon rate, then multiply by the number of days from the last payment date to settlement, divided by the number of days in the payment period under the bond’s day count convention. A $10,000 corporate bond paying 5% semiannually with a 30/360 convention and 45 days since the last coupon carries about $62.50 in accrued interest ($10,000 × 0.05 × 45/360).
Tax matters here. Your broker reports the full coupon payment on Form 1099-INT, which makes it look like all of that interest is your taxable income. It isn’t. The portion you paid the seller is a return of your own capital.5Internal Revenue Service. Publication 550 – Investment Income and Expenses Report the full 1099-INT figure on Schedule B, then subtract the accrued interest you paid, labeling the deduction “Accrued Interest” below the subtotal.6Internal Revenue Service. Instructions for Schedule B (Form 1040) Skip that step and you’ll overpay by the amount that rightfully belonged to the seller.
IRS Underpayment Interest
The IRS charges accrued interest on unpaid taxes, and the math works against you. For the first quarter of 2026, the individual underpayment rate is 7%, compounded daily.7Internal Revenue Service. Interest Rates Remain the Same for the First Quarter of 2026 That rate has held steady through 2025 and into 2026.8Internal Revenue Service. Quarterly Interest Rates Large corporate underpayments face 9%.
Because the IRS compounds daily rather than monthly or quarterly, a tax debt grows faster than most people expect. On a $10,000 underpayment at 7% compounded daily, roughly $1.92 accrues every day. Over six months that adds up to about $350, and the interest itself starts generating more interest. Plug the IRS rate into the compound formula above with n = 365 to see what you’ll owe by the time you pay.
A Note on Reporting Interest Income
Most individuals use the cash method for taxes, which means interest counts as income in the year you receive it or it’s credited to your account.9Internal Revenue Service. Publication 538 – Accounting Periods and Methods Interest a bank credits to your savings account in December is income for that year, even if you don’t withdraw it until March. Financial institutions must send you Form 1099-INT or 1099-OID if the interest or original issue discount credited to you totals $10 or more.10Internal Revenue Service. Guide to Original Issue Discount (OID) Instruments You’re required to report the income whether or not you receive a form, and running your own accrued interest calculations lets you cross-check the numbers before filing.