To calculate interest on a loan, you need three numbers from your paperwork — the principal, the annual interest rate, and the loan term — and the right formula for your loan type. Simple interest loans use one quick multiplication. Compound interest loans use an exponent that reflects how often interest is added to the balance. Amortized loans like mortgages and auto loans use a payment formula, and the interest portion of each monthly payment shifts as the balance drops. Credit cards run on a daily method of their own. The arithmetic in each case is straightforward once you have the inputs lined up.
Pull These Four Numbers First
Every formula below runs on the same raw inputs. Before you touch a calculator, find these on your loan documents or latest statement:
- Principal: the original amount borrowed, or your current outstanding balance if you want to know interest going forward. Your most recent statement is the reliable source for a current balance.
- Annual interest rate: the yearly rate as a percentage, which you convert to a decimal before using. Divide by 100, so 6% becomes 0.06 and 12.5% becomes 0.125.
- Loan term: how long you have to repay, usually in months or years. A 30-month loan is 2.5 years when a formula asks for years.
- Compounding frequency: how often interest is calculated and added to the balance — annually, monthly, daily, or some other interval. This matters for compound interest and does not affect simple interest.
Federal law requires lenders to put these numbers in front of you. The Truth in Lending Act requires that the annual percentage rate and finance charge be disclosed more prominently than any other loan term, so they are easy to spot on the paperwork.1Office of the Law Revision Counsel. 15 U.S. Code 1632 – Form of Disclosure; Additional Information
Use the Nominal Rate, Not the APR
Your paperwork lists two rates that look similar but measure different things. The nominal interest rate is the cost of borrowing the money itself. The annual percentage rate (APR) folds in origination fees, closing costs, mortgage insurance, and broker fees to show the total annual cost of the loan. Federal law defines the APR as the rate that, applied to your unpaid balances by an actuarial method, produces a sum equal to the total finance charge.2Office of the Law Revision Counsel. 15 USC 1606 – Determination of Annual Percentage Rate
For the formulas below, use the nominal rate. That is the number that drives actual interest charged each period. The APR is for comparing two offers side by side, because it captures fees one lender bundles in that another might not. A loan at 5.5% with heavy origination fees can carry a higher APR than one at 5.75% with no fees.
Simple Interest
Simple interest accrues only on the original principal, never on previously accumulated interest. The formula:
I = P × r × t
Say you borrow $10,000 at 5% for three years. Multiply $10,000 by 0.05 to get $500 in annual interest, then multiply by 3 years. Total interest over the life of the loan: $1,500. For a loan shorter than a year, express time as a fraction. Six months is 0.5. Ninety days is either 90/365 or 90/360, depending on which day-count convention your lender uses.
The 360-Day vs. 365-Day Year
Not all lenders count days the same way. Some use a 360-day year, sometimes called the banker’s year, and others use the actual 365-day calendar year. The difference is small on a single payment and larger over time. On a $100,000 loan at 6% held for 90 days, the 360-day method produces $1,500 in interest (100,000 × 0.06 × 90/360), and the 365-day method produces about $1,479 (100,000 × 0.06 × 90/365). Credit card issuers generally divide by either 360 or 365 depending on the issuer.3Consumer Financial Protection Bureau. What Is a Daily Periodic Rate on a Credit Card Check your cardholder agreement or promissory note for the convention being used, because it affects every calculation you run.
Compound Interest
Most real-world loans compound. Interest accrues on the principal and on any interest already added to the balance. The formula:
A = P × (1 + r/n)^(n × t)
A is the total amount owed at the end, P is the principal, r is the annual rate as a decimal, n is how many times per year interest compounds, and t is the number of years.4Investor.gov. Compound Interest Calculator To find just the interest cost, subtract the original principal: Total Interest = A − P.
Take a $15,000 loan at 8% compounded monthly for 5 years. The monthly rate is 0.08/12 = 0.00667, and you have 60 compounding periods (12 × 5). A = 15,000 × (1.00667)^60 ≈ $22,325. About $7,325 of that is interest, noticeably more than the $6,000 simple interest on the same loan.
Why Compounding Frequency Matters
The more often interest compounds, the more you pay. At a nominal 18% annual rate, the effective rate shifts with the compounding period. Annual compounding keeps the rate at 18%. Quarterly compounding pushes it to about 19.25%. Monthly compounding reaches roughly 19.56%. Daily compounding comes in near 19.72%. The jump from annual to monthly compounding adds more than a full percentage point to the effective rate on an 18% loan. At lower rates the gap narrows, but it never disappears. Two loans at the same nominal rate can cost different amounts, with the one compounding daily producing more interest than the one compounding monthly.
Monthly Payment on an Amortized Loan
Mortgages, auto loans, and most personal loans amortize. Each fixed monthly payment covers that month’s interest plus a slice of principal, and the interest portion shrinks as the balance drops. The formula for the fixed monthly payment:
M = P × [r(1 + r)^n] / [(1 + r)^n − 1]
M is the monthly payment, P is the loan principal, r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments. On a $200,000 mortgage at 6% for 30 years, r = 0.005 and n = 360. The payment works out to about $1,199 per month.
How Each Payment Splits Between Interest and Principal
To find the interest portion of any single month’s payment, multiply the current outstanding balance by the monthly rate. On that same $200,000 mortgage, the first month’s interest is $200,000 × 0.005 = $1,000. Since the total payment is $1,199, the remaining $199 reduces principal. Next month, the balance is $199,801, so interest drops to about $999, and an extra dollar shifts to principal.
Early in the loan, most of your payment is interest. By year 20 of a 30-year mortgage, principal dominates. Tracking the split lets you verify your lender’s math and see your actual equity-building progress rather than relying on the lender’s portal.
When Your Balance Grows Despite Payments
Some loan structures allow a minimum payment that does not cover the full interest charge for the month. The unpaid interest gets added to principal, and you end up owing more than you borrowed.5Consumer Financial Protection Bureau. What Is Negative Amortization This is negative amortization. Qualified mortgages under federal rules cannot include negative amortization features, so most conventional home loans are protected.6Consumer Financial Protection Bureau. Ability-to-Repay and Qualified Mortgage Rule Compliance Guide Adjustable-rate loans, payment-option mortgages from non-QM lenders, and some student loan repayment plans can still produce it. If your balance is climbing despite monthly payments, your payment is not covering the interest, and you need to raise it at least to the full interest amount to stop the growth.
Credit Card Interest
Credit cards run on a daily calculation that works differently from installment loans. Three steps: find the daily rate, find your average daily balance, multiply.
Divide your APR by 365 (or 360, depending on the issuer) to get the daily periodic rate.3Consumer Financial Protection Bureau. What Is a Daily Periodic Rate on a Credit Card An 18% APR divided by 365 gives a daily rate of about 0.0493%. Next, calculate the average daily balance by adding the balance at the end of each day in the billing cycle and dividing by the number of days. Some issuers include new purchases in that calculation and others exclude them, and your cardholder agreement specifies which method applies.7Consumer Financial Protection Bureau. Regulation Z 1026.7 – Periodic Statement Multiply the average daily balance by the daily rate, then by the number of days in the billing cycle (typically 28 to 31).
If your average daily balance is $3,000, your daily rate is 0.000493, and the cycle is 30 days, the finance charge is $3,000 × 0.000493 × 30 = $44.37. This is why mid-cycle payments help. A $500 payment on day 10 lowers your average daily balance for the remaining 20 days and reduces the interest that accrues, even though the due date has not arrived.
Grace Periods Can Zero Out the Interest
Most cards offer a grace period between the end of the billing cycle and the payment due date. Pay the full statement balance by the due date and you owe no interest on purchases.8Consumer Financial Protection Bureau. What Is a Grace Period for a Credit Card Issuers must send the bill at least 21 days before payment is due.
Carry a balance past the due date and you lose the grace period on new purchases too. Interest begins accruing on each new transaction from the date it posts, not from the next billing cycle. Cash advances and balance transfers typically have no grace period at all, and interest starts immediately. Restoring the grace period means paying the full balance to zero, which can take two consecutive cycles of full payment depending on the issuer.
Use the Math to Check Statements and Plan Extra Payments
Once you can run the formulas, you can catch errors. For an amortized loan, multiply your current balance by the monthly rate and compare the result to the interest line on your statement. If the numbers do not match within a few cents, something is off: a payment that was not applied on the date you sent it, or a rate change on a variable-rate loan that the servicer handled differently than your agreement specifies. For a credit card, reconstruct the average daily balance from your transaction history. It is tedious, and it is the only way to confirm the finance charge.
The same arithmetic shows what extra payments save. Because amortized interest is recalculated on the remaining balance each month, every extra dollar toward principal cuts all future interest charges. On a $200,000 mortgage at 4% for 30 years, adding $100 per month toward principal can shorten the loan by more than four years and eliminate over $26,000 in interest. Doubling that to $200 extra per month cuts roughly eight years and saves more than $44,000. When sending extra, tell the servicer to apply it to principal. Some will otherwise apply it to the next month’s scheduled payment, which does not reduce the balance any faster than the original schedule.
For a borrower who comes into a lump sum, a mortgage recast is worth asking about. You make a large principal payment and the lender recalculates the monthly payment on the lower balance, keeping the same rate and remaining term. A recast does not require an appraisal, credit check, or closing costs, though most lenders charge a small administrative fee and require a minimum lump sum. Federal law restricts prepayment penalties on qualified mortgages, so most borrowers can make extra payments without triggering a fee.