Simple and compound interest produce dramatically different results over time. Here are both formulas, worked examples, and the precise point where compound interest starts to dominate.
Interest is the cost of borrowing money — or the reward for lending it. Two fundamentally different methods of calculating it produce wildly different outcomes over time, and understanding both is essential for any financial decision.
Simple interest is calculated only on the original principal. It doesn't compound — you earn (or pay) the same amount each period regardless of accumulated interest.
Simple interest is used for short-term loans, some bonds, and straightforward hire-purchase agreements. It's predictable and easy to calculate.
Compound interest calculates interest on the principal plus any previously accumulated interest. You earn interest on your interest — and the effect grows exponentially over time.
More frequent compounding earns more — but the difference between monthly and daily is small. The big jump is from simple to compound, and from annual to more frequent compounding.
After 40 years, compound interest produces more than three times as much as simple interest on the same principal at the same rate. This divergence is why starting to invest early matters so profoundly.
At the mathematical limit — infinitely frequent compounding — we reach continuous compounding, which uses Euler's number (e):
Continuous compounding produces only slightly more than daily compounding — the practical difference is negligible. It's primarily used in theoretical finance and physics.