Formula without contributions
A = P(1 + r/n)^(nt)
Variables
- A: future value.
- P: starting principal.
- r: annual interest rate as a decimal.
- n: compounding periods per year.
- t: time in years.
Worked example
For 1,000 at 6% compounded annually for 2 years: A = 1000 x (1 + 0.06/1)^(1 x 2) = 1,123.60. The interest earned is 123.60.
What compounding frequency changes
With the same nominal annual rate, monthly compounding adds interest 12 times per year, while annual compounding adds it once. The difference is often small at low rates and short time periods, but it becomes more visible over longer horizons.
Contributions need an extra assumption
Recurring contributions are not handled by the basic formula alone. A calculator must decide whether contributions happen at the beginning or end of each period, and whether they compound immediately. Those timing choices change the final value.
When the formula is not enough
- Investment returns are not usually constant or guaranteed.
- Fees, taxes and inflation can materially reduce real returns.
- Variable rates, irregular deposits and withdrawals require a cash-flow model rather than a single closed formula.
References
- Investor.gov: Compound interest - investor education context, accessed 2026-05-17.