How compound interest actually works
The plain-English version of the formula every finance article quotes — and a feel for why it gets dramatic over decades.
5 min readReviewed Apr 1, 2026
Quick answer
Each period, interest is added to your balance. Next period, you earn interest on the new, slightly larger balance. The longer you let it run, the more lopsided the curve gets.
The formula
The compound interest formula is A = P × (1 + r/n)^(n·t). P is what you start with, r is your annual rate, n is how many times a year interest compounds, and t is years.
If interest compounds once a year, n = 1 and the formula collapses to A = P × (1 + r)^t. That's the version most people memorize.
Why it bends upward
1. Year one
You earn interest on P. Balance becomes P × (1 + r).
2. Year two
You earn interest on P × (1 + r). Balance becomes P × (1 + r)^2.
3. Year t
Balance is P × (1 + r)^t. The exponent is what bends the curve.