Figuring interest comes down to three pieces of information: the amount of money involved (the principal), the interest rate, and the length of time. The exact method depends on whether you’re dealing with a savings account, a credit card, a car loan, or a mortgage, but every interest calculation builds on those same three variables. Here’s how to work through each one.
The Simple Interest Formula
Simple interest is the most straightforward calculation. You multiply the principal by the interest rate by the time period:
Interest = Principal × Rate × Time
If you borrow $5,000 at 6% annual interest for 3 years, the math is $5,000 × 0.06 × 3 = $900 in total interest. The key feature of simple interest is that it’s calculated only on the original amount. Your balance doesn’t grow from accumulated interest, so the charge stays predictable. Some short-term personal loans and auto loans use simple interest.
When plugging in the rate, convert the percentage to a decimal first. A 6% rate becomes 0.06. And make sure the time unit matches the rate. If the rate is annual, express time in years. A 6-month loan at an annual rate of 8% would use 0.5 for the time: $10,000 × 0.08 × 0.5 = $400.
How Compound Interest Works
Compound interest is what most savings accounts, investments, and many loans actually use. Instead of charging interest only on the original principal, it charges interest on the principal plus any interest that has already accumulated. In other words, you earn (or owe) interest on your interest.
The formula looks like this:
Compound Interest = P × (1 + i)n − P
P is the principal, i is the interest rate per compounding period, and n is the total number of compounding periods. If you have a $10,000 savings account earning 4% interest compounded monthly, the rate per period is 0.04 ÷ 12 = 0.00333. Over one year (12 periods), you’d calculate $10,000 × (1.00333)12 − $10,000 = about $407. That’s slightly more than the $400 you’d earn with simple interest at the same rate, and the gap widens over time.
The frequency of compounding matters. Interest can compound daily, monthly, quarterly, or annually, and more frequent compounding produces more total interest. Over 10 years, a $100,000 deposit earning 5% with simple interest would generate $50,000 in total interest. That same deposit compounded monthly at 5% would produce roughly $64,700. The difference grows dramatically with larger balances and longer time horizons.
APR vs. APY: Which Number to Use
You’ll see two different rates quoted on financial products, and using the wrong one will throw off your calculation. APR (annual percentage rate) is the rate you pay when borrowing. It includes certain fees but does not account for compounding. APY (annual percentage yield) is the rate you earn on savings, and it does factor in compounding.
This distinction matters in practice. A credit card with an 18% APR actually costs more than 18% per year if you carry a balance, because the interest compounds. A savings account advertising a 4.5% APY already reflects the boost from compounding, so what you see is what you’ll actually earn over a year. When you’re figuring interest on debt, start with the APR and apply compounding yourself. When you’re estimating earnings on savings, the APY gives you the more accurate picture directly.
Figuring Interest on a Credit Card
Credit card interest is more involved than a simple formula because your balance changes throughout the month as you make purchases and payments. Most issuers use the average daily balance method, which works in three steps.
First, find your daily periodic rate. Take your card’s APR and divide by 365. A card with a 20% APR has a daily rate of about 0.0548% (0.20 ÷ 365 = 0.000548).
Second, calculate your average daily balance. The issuer tracks your balance every day of the billing cycle, adding new charges and accrued interest while subtracting payments and credits. All those daily balances get added together, then divided by the number of days in the billing cycle. If your daily balances over a 30-day cycle add up to $32,000, your average daily balance is $1,066.67.
Third, multiply it all together: average daily balance × daily periodic rate × number of days in the billing cycle. Using the example above, that’s $1,066.67 × 0.00055 × 30 = $17.60 in interest for the month. On a higher balance, this adds up quickly. A $5,000 average daily balance on a 22% APR card would cost roughly $90 in a single month.
One important detail: if you pay your full statement balance by the due date each month, most cards give you a grace period and charge no interest at all. The calculation above only kicks in when you carry a balance.
Interest on Mortgages and Car Loans
Mortgages, car loans, and most other installment loans use amortization. Your monthly payment stays the same, but the split between interest and principal shifts over the life of the loan.
Each month, the lender calculates interest on your current outstanding balance at one-twelfth of the annual rate. If you owe $200,000 on a mortgage at 6.5%, your first month’s interest is $200,000 × (0.065 ÷ 12) = $1,083.33. If your monthly payment is $1,264, only about $181 goes toward reducing the principal that first month. The rest is interest.
As you pay down the balance, less of each payment goes to interest and more goes to principal. By the final years of a 30-year mortgage, nearly the entire payment is principal. This is why making extra payments early in a loan saves you the most money: you reduce the balance that interest is calculated on for every remaining month.
To see exactly how much interest you’ll pay over the full life of a loan, you can build an amortization schedule. For each month, calculate that month’s interest (outstanding balance × monthly rate), subtract it from your fixed payment to find the principal portion, then subtract the principal portion from your balance. Repeat for every month. Online amortization calculators do this instantly, but understanding the underlying math helps you evaluate whether refinancing or making extra payments is worth it.
Quick Reference for Common Scenarios
- Savings account: Use the compound interest formula with the compounding frequency your bank specifies (usually daily). Or simply multiply your balance by the APY to estimate one year of earnings.
- Credit card: Divide the APR by 365 for the daily rate, find your average daily balance, and multiply by the number of days in the billing cycle.
- Mortgage or car loan: Multiply your current balance by one-twelfth of the annual rate to find how much interest you owe in any given month.
- Short-term personal loan: If the lender uses simple interest, multiply principal × rate × time. Make sure the time unit matches the rate (annual rate needs time in years).
Regardless of the type, the core logic never changes. Interest is always the cost of using someone else’s money (or the reward for letting someone use yours), calculated as a percentage of the balance over a period of time. The differences are just in how often interest gets recalculated and whether it compounds on itself.