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Use the compound interest formula A = P(1 + r/n)^(nt) to calculate future value. Enter principal, rate, time, and compounding frequency for instant results.
The compound interest formula A = P(1 + r/n)^(nt) has four variables: P = principal (initial amount), r = annual interest rate (decimal), n = number of times interest compounds per year, and t = time in years. A is the final amount. For example, $5,000 at 6% compounded quarterly for 10 years: A = 5000(1 + 0.06/4)^(4×10) = 5000(1.015)^40 = 5000 × 1.8140 = $9,070.09.
The value of n depends on compounding frequency: annually (n=1), semi-annually (n=2), quarterly (n=4), monthly (n=12), daily (n=365). For continuous compounding, use the formula A = Pe^(rt), where e ≈ 2.71828. On $10,000 at 5% for 10 years: annual gives $16,289, monthly gives $16,470, daily gives $16,487, and continuous gives $16,487.21.
A = final amount, P = principal (starting amount), r = annual interest rate as a decimal (e.g., 5% = 0.05), n = compounding frequency per year (12 for monthly, 365 for daily), t = time in years. The formula calculates the total balance including both principal and earned interest.
Divide the annual percentage rate by 100 to get the decimal form: 5% becomes 0.05, 7.5% becomes 0.075, 12% becomes 0.12. Then divide by n (compounding periods) in the formula. For 6% compounded monthly: r/n = 0.06/12 = 0.005 per period.
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