Formula reference

Compound Interest Formula

These formulas explain the math used by compound interest calculators. They are planning formulas, not predictions of real investment returns.

One-time principal

A = P(1 + r / n) ^ (nt)

Use when there are no extra deposits.

Effective annual yield

APY = (1 + r / n) ^ n - 1

Use to compare rates with different compounding schedules.

Monthly projection

B = B(1 + monthlyRate) + C

Use when contributions happen monthly.

Decision guide

Choose the formula that matches the cash flow

The familiar formula A = P(1 + r/n)^(nt) models one starting principal with a constant nominal annual rate. Additions and withdrawals need a cash-flow term or a period-by-period schedule. Rate changes, taxes, fees, inflation, and market volatility are outside the basic formula and should be modeled as separate scenarios.

$10,000 for ten years at 5%

With annual compounding, P is 10,000, r is 0.05, n is 1, and t is 10. The formula gives about $16,288.95. That is a mathematical projection, not a guaranteed return. A savings account rate may change, while an investment can rise or fall and may not compound at a fixed rate.

Before you decide

  • Use 0.05 in the formula for 5%.
  • Keep rate and compounding periods in matching units.
  • Place deposits at the correct beginning or end of each period.
  • Run low, expected, and high-rate scenarios.

Method and limitations

Investor.gov separates initial principal, contributions, time, rate, variance, and compounding frequency because each changes the result. Our focused formulas are educational shortcuts. For a real account, reconcile the projection with the product disclosure, statement-crediting method, fees, and tax treatment.