How the Compound Interest Calculator works
The full formula, every assumption, and the authority each piece comes from — so you can verify the math before you trust it with a retirement decision.
The formula
FriendlyCalc's compound interest calculator uses the standard closed-form expression published by the U.S. Securities and Exchange Commission on Investor.gov:
A = P × (1 + r / n)n · t
- A — the final balance after t years.
- P — the starting principal.
- r — the annual interest rate, expressed as a decimal (enter 7 in the calculator, we divide by 100).
- n — the number of compounding periods per year: 1 (annual), 2 (semi-annual), 4 (quarterly), 12 (monthly), or 365 (daily).
- t — the number of years the money is invested.
The Effective Annual Rate (APY)
Shown alongside the final balance, this is the rate that an annually-compounded account would need to pay to match whatever compounding frequency you selected:
APY = (1 + r / n)n − 1
The Consumer Financial Protection Bureau uses this same definition when describing APY and compounding frequency. APY is the apples-to-apples number for comparing savings accounts and CDs.
What this calculator assumes
- The annual rate is fixed for the entire period. Real-world rates on savings accounts and bonds move; this tool does not model that.
- There are no additional contributions and no withdrawals between deposit and final balance. For recurring contributions, use the Investment Calculator.
- No taxes or fees are subtracted while compounding. In a taxable account, the effective rate is lower because interest and dividends are taxed each year; see IRS Topic 409.
- No inflation adjustment. The balance shown is nominal. To see real purchasing power, subtract your inflation assumption from the rate, or run the result through the Inflation Calculator.
- "Daily" compounding uses a 365-day year. Some financial institutions use 360; the difference is negligible over long horizons and we favor the 365 convention that Investor.gov uses.
Edge cases
- Zero rate. If you enter a 0% rate, the formula collapses to A = P. The interest line correctly reads $0.
- Fractional years. The calculator accepts non-integer years (e.g. 7.5). The exponent n·t becomes non-integer, which is still well-defined.
- Very high rates over long horizons. At extreme inputs (say 40% over 50 years) the final balance becomes astronomically large. The formula is still correct; the inputs are just unrealistic. This is a math tool, not a sanity filter.
Sources and authorities
Reviewed by the FriendlyCalc Math & Editorial Team.
Last methodology update: 2026-04 · Next review due: 2027-04
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