How compound interest works
With compound interest, the interest you earn is added to your balance and starts earning interest itself. Over long periods this snowball effect is what makes saving and investing early so powerful.
A = P·(1 + i)ⁿ + PMT·[(1 + i)ⁿ − 1] / i
P is the initial deposit, PMT the regular contribution, i the rate per period (the annual rate divided by 12 if it compounds monthly) and n the number of periods.
Example · $5,000 plus $200 a month at 6% for 20 years
Monthly rate i = 0.5%, n = 240. The initial $5,000 grows to 5,000 × 1.005²⁴⁰ = $16,551. The contributions grow to 200 × (1.005²⁴⁰ − 1) / 0.005 = $92,408. Final balance ≈ $108,959, of which $53,000 is what you put in and about $55,959 is interest.
The rule of 72
A quick way to estimate how long it takes to double your money: divide 72 by the annual interest rate. At 6% it takes about 12 years; at 9%, about 8.
Inflation and real returns
A balance in 20 years will not buy what the same amount buys today. Enter an inflation rate to see the final balance in today's money: that is your real gain.
Frequently asked questions
Is this the same as APY?
APY (annual percentage yield) is the effective annual return once compounding is included. With monthly compounding, a 6% nominal rate gives an APY of about 6.17%.
Does it include taxes and fees?
No. Investment fees and taxes on interest or gains reduce the real result. Lower the interest rate to approximate them.
How much do I need to save each month for a goal?
Use the savings goal calculator.
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