The compound interest formula
Compound interest means each period's interest is added to the balance, so the next period earns interest on a larger amount. For a single deposit:
A = P(1 + r/n)^(n·t)
With regular monthly contributions PMT, the future value of the contributions is added:
FV = PMT × [(1 + i)^m − 1] ÷ i
- P — initial deposit; r — annual rate; n — compounding periods per year; t — years
- i — effective monthly rate, (1 + r/n)^(n/12) − 1; m — number of monthly contributions
Worked example
$10,000 invested at 5% compounded annually for 10 years becomes 10,000 × 1.05¹⁰ = $16,288.95. Add $200 a month and the total rises to roughly $47,400 — of which about $10,000 is pure interest on your contributions.
Key terms
- APY / AER
- Annual percentage yield (US) or annual equivalent rate (UK) — the true yearly return after compounding.
- Compounding frequency
- How often interest is credited. More frequent compounding yields slightly more, but the effect is small compared with rate and time.
- Rule of 72
- Divide 72 by the annual rate to estimate how many years it takes to double your money. At 6%, roughly 12 years.
- Tax-advantaged accounts
- 401(k)s and IRAs (US), ISAs and pensions (UK), and TFSAs and RRSPs (Canada) let returns compound with reduced or no tax.