The formula
A = P · (1 + r/n)^(n·t), where A is the final amount, P the principal, r the annual rate, n the compounding frequency per year, and t the number of years. For monthly compounding n = 12.
Why time beats rate
Doubling the annual rate doubles the rate of growth, but doubling the time-horizon roughly squares the final amount because compounding is exponential. The practical takeaway: starting earlier almost always beats trying to chase yield later.
Where the model breaks
Real-world returns are not constant — markets fluctuate, inflation erodes purchasing power, taxes reduce net returns. Use compound interest as a planning baseline, not a promise.