Compound Interest Explained: The Math Behind Long-Term Wealth

The Compound Interest Formula

The standard formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal you start with, r is the annual interest rate (as a decimal), n is the number of times interest compounds per year, and t is the number of years.

If you add regular contributions, the formula extends with a future-value-of-an-annuity term. Our compound interest calculator handles both cases automatically.

A Real Example

Imagine you invest $10,000 at a 7% average annual return, compounded monthly, for 30 years. The formula gives A = 10000 × (1 + 0.07/12)^(12×30) ≈ $81,164. You put in $10,000 once and it grew more than eightfold without you adding a cent.

Now add $200 a month. Over the same 30 years your contributions total $72,000 — but the final balance climbs to roughly $325,000 thanks to compounding on every contribution.

Why Starting Early Wins

Two friends each invest at 7%. Anna starts at 25 and saves $200/month until 35, then stops contributing forever. Ben starts at 35 and saves $200/month every month until 65. Anna invested $24,000 total; Ben invested $72,000. At age 65, Anna has more money. That's the magic of an extra ten years of compounding.

The earlier you start, the more years your interest has to earn its own interest. Time matters more than amount for most investors.

The Rule of 72

A handy shortcut: divide 72 by your annual return to estimate how many years it takes your money to double. At 6%, money doubles in about 12 years. At 9%, in about 8 years.