To calculate interest charges on loans and cards, you need three numbers from your statement or loan agreement: the principal balance, the interest rate expressed as a decimal, and the length of time the balance is outstanding. Which formula you plug them into depends on the product. A personal loan between individuals usually uses simple interest. A credit card uses the average daily balance method with a daily periodic rate. A mortgage or auto loan uses an amortization schedule that recalculates interest on a shrinking balance every month. Savings accounts and some loans compound, meaning interest earns interest.
Pull the Three Numbers First
Open your loan agreement or statement and find the principal (what you borrowed or currently owe), the annual interest rate, and the time period the calculation covers. Federal disclosure rules require lenders to present these figures in a clear, standardized format so you don’t have to hunt through fine print.1Consumer Financial Protection Bureau. 1026.17 General Disclosure Requirements
Two conversions trip people up. Divide the annual percentage rate by 100 to turn it into a decimal: 6% becomes 0.06. Then make sure the rate and the time period use the same units. If the rate is annual and you’re measuring six months, express the time as 0.5 years. Mix the units and the answer comes out wildly off.
Simple Interest
Multiply the principal by the decimal rate by the number of years. Borrow $5,000 at 6% for three years and the interest is $5,000 × 0.06 × 3 = $900. The balance never changes during the calculation, so interest never stacks on itself.
This is the method behind short-term personal loans, many auto loans, certificates of deposit, and informal loans between individuals. It generates less total interest than compounding at the same rate, which is why most banks and card issuers use something else.
Compound Interest
Compound interest charges interest on the original balance plus any interest already accrued. You need a fourth number: how many times per year the interest compounds (monthly, daily, quarterly).
The math: divide the annual rate by the compounding frequency, add 1, raise the sum to the power of the frequency times the number of years, then multiply by the principal. The result is the ending balance. Subtract the original principal to isolate the interest.
Frequency matters more than it looks. A $10,000 balance at 8% compounded annually earns $800 in the first year. Compounded monthly, it earns about $830. Compounded daily, slightly more. Banks must disclose the compounding frequency on deposit accounts and publish an annual percentage yield so you can compare accounts on equal footing.2eCFR. 12 CFR Part 1030 – Truth in Savings (Regulation DD)
Credit Card Interest: Average Daily Balance
Credit card issuers don’t wait until the end of the cycle. Most calculate interest daily using the average daily balance method.3Consumer Financial Protection Bureau. How Does My Credit Card Company Calculate the Amount of Interest I Owe?
Three steps:
- Find the daily periodic rate by dividing the card’s APR by 365 (some issuers use 360). An 18% APR works out to about 0.0493% per day.4Consumer Financial Protection Bureau. What Is a Daily Periodic Rate on a Credit Card?
- Add up your balance for each day of the billing cycle (purchases raise it, payments drop it) and divide by the number of days. That’s the average daily balance.
- Multiply the average daily balance by the daily rate, then by the number of days in the cycle. That’s your finance charge.
Run the numbers. A $2,000 average daily balance on a card with a 0.0493% daily rate over a 30-day cycle generates roughly $29.59 in interest. This also explains why a mid-cycle payment reduces the charge: each day you carry a lower balance pulls the average down.
Federal law requires the card issuer to print the applicable periodic rates and the APR on every billing statement so you can verify the math.5Office of the Law Revision Counsel. 15 USC 1637 – Open End Consumer Credit Plans
Installment Loans and Amortization
For a mortgage, auto loan, or any fixed-payment loan, the fastest way to find total interest is arithmetic: multiply your monthly payment by the number of payments, then subtract the original loan amount. A $1,500 monthly payment over 30 years is 360 payments totaling $540,000. If you borrowed $300,000, that’s $240,000 in interest across the loan. Lenders must show this “total of payments” figure before you close.6eCFR. 12 CFR 1026.18 – Content of Disclosures
That total hides a detail that matters if you want to check any single month’s charge. Each month, the lender multiplies the remaining balance by the monthly rate (annual rate divided by 12). Whatever’s left of your payment after that interest comes off the principal.
Walk through month one of a $300,000 mortgage at 6%. The monthly rate is 0.005. Interest for the first month is $300,000 × 0.005 = $1,500. If the payment is $1,798, only $298 goes to principal. Next month the balance is slightly smaller, so slightly less goes to interest and slightly more to principal. This is why early mortgage years feel so slow for equity: the interest share is largest when the balance is largest.
Interest Rate vs. APR
Your paperwork lists both an interest rate and an APR, and they aren’t the same number. The interest rate reflects only the cost of borrowing the principal. The APR adds in origination fees, broker charges, discount points, and other costs, giving you a yearly figure that captures what the loan actually costs.7Consumer Financial Protection Bureau. What Is the Difference Between a Mortgage Interest Rate and an APR?
Which to use depends on what you’re doing. For the dollar amount of interest on this month’s balance, use the interest rate. For comparing two offers from different lenders, use the APR, because it levels out the fees one charges that another may not.
Variable Rates: Index Plus Margin
Adjustable-rate mortgages and some other loans don’t lock in one rate. The rate is built from an index (a market benchmark that moves) plus a margin (a fixed number of percentage points set in your loan agreement).8Consumer Financial Protection Bureau. For an Adjustable-Rate Mortgage (ARM), What Are the Index and Margin, and How Do They Work? Add them. If the index is 4.5% and your margin is 2%, the current rate is 6.5%. After each adjustment, plug the new combined rate into whichever formula applies to your loan.
What Rate a Lender Can Legally Charge
Not every rate a lender might want is legal, though the ceilings are looser than most borrowers assume. Most states cap interest on certain consumer loans through usury laws, and when a written agreement doesn’t specify a rate, a state’s default legal rate (often between 5% and 10%) fills the gap.
Nationally chartered banks sit outside most state caps. Federal law lets them charge the maximum permitted in the state where the bank itself is located, regardless of where the borrower lives.9Office of the Law Revision Counsel. 12 USC 85 – Rate of Interest on Loans, Discounts and Purchases This is why credit card APRs often reach 25% or higher.
Active-duty service members and their dependents have a firm federal cap. The Military Lending Act limits the rate on most consumer credit to 36%, calculated as a Military Annual Percentage Rate that folds in finance charges, credit insurance premiums, and certain fees.10Office of the Law Revision Counsel. 10 USC 987 – Terms of Consumer Credit Extended to Members and Dependents A loan to a covered borrower that exceeds the cap is void.
If the Numbers Don’t Match
Run the formula that fits your product. If the result doesn’t line up with what your card issuer or lender charged, you have the right to dispute it. The Fair Credit Billing Act requires card issuers to investigate billing errors, including computation errors, and credit back any finance charges that were wrongly applied.11Office of the Law Revision Counsel. 15 USC 1666 – Correction of Billing Errors Put the dispute in writing and keep a copy of your own calculation.