Interest Formula: Simple, Compound, and APR Math Explained
The interest formula you use depends on the product. A car loan uses simple interest. A high-yield savings account compounds daily. A credit card uses an average daily balance with daily compounding. Knowing which formula applies tells you exactly what you'll earn or owe.
Simple Interest Formula
Simple interest is calculated only on the original principal. It's used for most personal loans, auto loans, and short-term notes.
Formula: Interest = Principal × Rate × Time
Example: $10,000 at 8% APR for 5 years.
- Interest = $10,000 × 0.08 × 5 = $4,000
- Total repaid = $14,000.
With simple interest, paying extra principal early saves a proportional amount of interest. That's why aggressive early payments on an auto loan or personal loan move the needle quickly.
Compound Interest Formula
Compound interest is calculated on principal plus accumulated interest. It's how savings accounts, CDs, money market accounts, and credit cards work.
Formula: A = P × (1 + r/n)^(n×t)
Where A = final amount, P = principal, r = annual rate, n = compounding periods per year, t = years.
Example: $10,000 in a 4.50% APY savings account, compounded daily, for 5 years.
- A = $10,000 × (1 + 0.045/365)^(365×5) = $12,523
- Interest earned = $2,523.
Compare that to simple interest at the same rate: $10,000 × 0.045 × 5 = $2,250. Compounding adds an extra $273 over 5 years — and the gap widens dramatically over longer time horizons.
APR vs. APY: What's the Difference?
- APR (annual percentage rate) is the simple interest rate, no compounding factored in. Loans quote APR.
- APY (annual percentage yield) factors in compounding. Savings accounts quote APY.
The more frequent the compounding, the bigger the gap between APR and APY. At 5% APR compounded daily, the APY is ~5.13%.
How Credit Card Interest Is Calculated
Credit cards use an average daily balance method with daily compounding. The formula:
- Daily periodic rate = APR ÷ 365.
- For each day in the cycle, add (balance × daily rate) to a running interest tally.
- At cycle end, the tally is your interest charge.
Example: $5,000 average daily balance, 22% APR, 30-day cycle.
- Daily rate = 0.22 ÷ 365 = 0.000603.
- Interest = $5,000 × 0.000603 × 30 = $90.41
That's why even small balances on credit cards add up fast — daily compounding amplifies the cost. Building credit with a no-interest or low-interest credit-builder product like the Self.Inc Credit Builder Account, the Self Visa® Credit Card, or the Current Build Card (0% APR) sidesteps the daily compound trap entirely.
Quick Rules of Thumb
- Rule of 72 — divide 72 by your annual rate to get the years it takes for compounded money to double. At 6%, 72/6 = 12 years.
- Doubling time at 4.5% APY — about 16 years to double a savings deposit.
- Credit card debt at 24% APR — the unpaid balance roughly doubles in 3 years if you make no payments.
Frequently Asked Questions
What's the difference between simple and compound interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus accumulated interest. Compounding accelerates returns on savings and accelerates costs on debt over time.
Why is APY higher than APR for the same rate?
APY factors in compounding; APR does not. A 5% APR compounded daily becomes a 5.13% APY. The more frequent the compounding (daily, monthly, quarterly), the larger the gap.
How is interest calculated on credit cards?
Credit cards use the average daily balance method with daily compounding. The issuer multiplies your average daily balance by the daily periodic rate (APR ÷ 365) by the number of days in the billing cycle. Pay your statement balance in full to avoid interest entirely — the grace period only applies to non-revolving balances.
Does paying extra on a loan reduce interest?
Yes, dramatically. On a simple-interest loan, extra payments go directly to principal, which lowers the base for future interest. On a compound-interest loan or credit card, the effect is even bigger because you're cutting off future compounding.
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