Compound interest, explained with real numbers

Future value equals present value times (1 + rate per period) raised to the number of periods. The mistake almost everyone makes is mixing an annual rate with monthly periods. If the quoted rate is 6% a year compounded monthly, the rate per period is 0.5% and the number of periods is 12 per year, not 1.

10,000 at 6% for 10 years compounded annually grows to 17,908. The same money compounded monthly reaches 18,194 - a 286 difference. Frequency helps, but far less than an extra percentage point of return would.

The nominal rate is the headline number. The effective annual rate is what you actually earn once compounding is applied: (1 + r/m)^m - 1, where m is the number of compounding periods a year. A nominal 6% compounded monthly is an effective 6.17%.

Effective rate is the only fair way to compare two products quoted on different compounding schedules. Ask for it explicitly when a lender or platform only advertises the nominal figure.

With monthly deposits, most of the early balance is your own money and most of the final balance is growth. Contributing 300 a month for 30 years at 7% puts in 108,000 and ends near 366,000 - the crossover where growth exceeds contributions typically arrives somewhere in the second decade.

That crossover is why the length of time invested does more work than the size of any single deposit, and why pausing contributions early costs more than pausing them late.

A single fixed rate assumes steady returns. Real markets deliver an average with variance around it, and the order of good and bad years matters once you start withdrawing. Treat a compound interest projection as a planning baseline, not a forecast.

Inflation is the other adjustment: subtract expected inflation from your rate to see the result in today's purchasing power rather than in nominal currency.