Accrued interest is the interest that has built up on a loan, credit balance, or investment since the last payment date but hasn’t been paid yet. The math is straightforward: principal balance times the annual interest rate times the fraction of the year that has elapsed. The tricky part is how “the fraction of the year” gets measured, because mortgages, credit cards, and bonds each count time a little differently. Once you see how that fraction works, statements and trade confirmations that used to look opaque start to make sense.
The Core Formula
Principal × Rate × Time. Principal is the outstanding balance the interest is being charged on. Rate is the annualized interest rate. Time is a fraction of a year, and that fraction is the variable that causes the most confusion.
Take a $10,000 balance at 6% for 90 days. Under a simple-interest calculation, the accrued interest is $10,000 × 0.06 × (90/365) = $147.95. Change any of the three inputs and the number moves. Change the way the days are counted, and it moves too.
Day-Count Conventions
Two conventions dominate consumer and bond finance:
- Actual/365 uses the real number of calendar days in the accrual period as the numerator and keeps 365 as the denominator regardless of leap years (a variant called Actual/365L uses 366 in leap years).
- 30/360 assumes every month has exactly 30 days and every year has 360. A bond accruing from January 15 to March 15 counts as 60 days under 30/360, even though the calendar shows 59.
The convention changes the dollar figure. A $100,000 loan at 5% accrues $13.70 per day under Actual/365 and $13.89 per day under 30/360. Small daily differences compound into meaningful annual ones.
Simple Versus Compound
Simple interest applies the rate only to the original principal. The balance the interest is calculated on never changes.
Compound interest applies the rate to the principal plus any interest that has already accrued and been added in. If interest compounds monthly, month two’s charge is calculated on month one’s ending balance, which includes month one’s interest. Most mortgages, credit cards, and savings accounts use some form of compounding, and over a long horizon it materially increases what you pay or earn.
Accrued Interest on Mortgages and Auto Loans
On a standard fixed-rate mortgage, interest typically accrues monthly. Each payment first covers the interest that has built up since the last payment, and only what’s left reduces principal. That’s why the early years of a 30-year mortgage feel like you’re barely moving the balance. On a $300,000 loan at 7%, the first month’s payment sends roughly $1,750 toward interest and only about $245 toward principal. The split gradually shifts as the balance falls.
Most mortgages include a grace period of about 15 days after the due date before a late fee applies. The grace period protects you from penalties, but for a standard monthly-accrual mortgage, paying on the first versus the tenth doesn’t change the interest portion of the payment.
Auto loans commonly accrue interest daily. Paying a few days early each month trims a small amount off the total interest over the life of the loan. Not dramatic on a five-year note, but real.
Student Loans and Capitalization
Federal student loans handle accrued interest in two very different ways. Direct Subsidized Loans get an interest subsidy from the government while you’re enrolled at least half-time, during the six-month grace period after leaving school, and during certain deferment periods. No interest accrues against you during those stretches.1Federal Student Aid. Federal Interest Rates and Fees
Direct Unsubsidized Loans accrue interest from the day the loan is disbursed, including all the time you’re in school. For the 2025–2026 academic year, undergraduate Direct Loans carry a fixed rate of 6.39%.1Federal Student Aid. Federal Interest Rates and Fees On a $20,000 unsubsidized loan, four years of in-school accrual can add over $5,000 before you make your first payment.
Then comes capitalization. When your repayment period begins, the accrued interest is added to your principal balance, and future interest is calculated on the larger amount. For federal loans held by the Department of Education, capitalization happens when a deferment ends on an unsubsidized loan and when a borrower leaves an income-based repayment plan under certain conditions.2Nelnet. Interest Capitalization Making interest-only payments during school or deferment prevents that from happening and is one of the simplest ways to lower the lifetime cost of the loan.
Credit Card Interest and Trailing Interest
Credit card interest works differently from installment loans. Many issuers use the average daily balance method: they track your balance each day of the billing cycle, factor in purchases, payments, and credits, average those daily balances, and apply a daily periodic rate derived from your APR.3Consumer Financial Protection Bureau. How Does My Credit Card Company Calculate the Amount of Interest I Owe?
A grace period can eliminate this entirely. If your card offers one and you pay your statement balance in full by the due date, no interest accrues on new purchases in the next cycle. Carry a balance, though, and you lose the grace period, and interest starts accruing on every new purchase from the transaction date. Card companies aren’t required to offer a grace period, but if they do, they have to send your bill at least 21 days before the due date.4Consumer Financial Protection Bureau. What Is a Grace Period for a Credit Card?
One common source of confusion: trailing interest, sometimes called residual interest. Because interest accrues daily, there’s a gap between the day your statement closes and the day your payment posts. Interest keeps building during that gap. Even if you pay the full statement balance, the next statement may show a small interest charge for those in-between days. It isn’t an error. One more full payment usually clears it.
Accrued Interest When Buying or Selling Bonds
Bonds pay coupon interest on a fixed schedule, usually every six months, but interest accrues every day between coupon dates. When a bond trades between payments, the buyer and seller have to split that interest.
The seller held the bond and earned interest since the last coupon. The buyer will collect the full upcoming coupon. So the buyer pays the seller for the interest that built up during the seller’s ownership, and the buyer effectively gets that money back when the next coupon lands.
Bond markets handle this by quoting a “clean price” that excludes accrued interest. The accrued interest is calculated separately using the day-count convention in the bond’s terms and added on to produce the “dirty price,” which is what the buyer actually pays. The clean price is what you compare across bonds; the dirty price is what settles the trade.
When Payments Don’t Cover the Interest: Negative Amortization
If a payment doesn’t cover the interest that accrued during the period, the unpaid portion gets added to your principal. You owe more after paying than you did before. Federal regulations define a negative amortization loan as one that allows a minimum payment covering only part of the accrued interest, producing an increasing principal balance.5Consumer Financial Protection Bureau. Regulation Z – 1026.18 Content of Disclosures
This can happen on certain adjustable-rate mortgages, payment-option loans, and some income-driven student loan repayment plans. It compounds on itself: as principal grows, monthly interest grows with it, making the shortfall worse. Borrowers who don’t realize their payments are insufficient can end up owing substantially more than they originally borrowed, sometimes more than the property securing the loan is worth. If a loan you’re considering allows a payment smaller than the interest charge, that’s the feature to ask about before signing.