Compound Interest Explained
Compound interest is interest earned on both your original money and the interest it has already earned. It is the engine behind long-term investing — and, on debt, the reason balances can balloon. Albert Einstein supposedly called it the eighth wonder of the world; the math is simple once you see it.
The compound interest formula
A = P(1 + r ÷ n)nt, where P is the principal, r is the annual rate (as a decimal), n is the number of times interest compounds per year, and t is the number of years. A is the final amount.
Simple vs compound interest
Simple interest is charged only on the original principal, so it grows in a straight line. Compound interest is charged on principal plus accumulated interest, so it curves upward and accelerates. Over a year or two the gap is small; over decades it is enormous. Compare them side by side with the compound interest calculator and the simple interest calculator.
How compounding frequency matters
The more often interest is added, the more you earn, because interest starts earning its own interest sooner. $10,000 at 6% for 10 years grows to about $17,908 compounded annually, but roughly $18,194 compounded monthly. More frequent compounding always helps the saver.
Why starting early wins
Time is the most powerful variable in the formula because it sits in the exponent. Money invested in your twenties has decades to compound, which is why an early, smaller investment often beats a later, larger one. The same effect powers monthly investing — see the SIP calculator for compounding on regular contributions.
- Higher rate → faster growth, magnified over time.
- More frequent compounding → slightly higher returns.
- More years → the single biggest driver of the final amount.
To measure what an actual investment returned per year, use the ROI calculator, which reports the annualized rate (CAGR).