Simple vs Compound Interest
Side-by-side interest model comparison.
Exponential Growth Dynamics 🖖
Continuous compounding converges to the natural exponential growth function...
Interest on interest 🖖
Simple interest pays a fixed amount every year based only on your starting principal, so the total climbs in a straight line. Compound interest also pays interest on the interest already earned, so each year's gain is slightly bigger than the last and the curve bends upward. With annual compounding both match after the first year; every bit of the widening gap is money that past interest earned on your behalf.
A penny from year zero 🖖
In 1772 the actuary Richard Price calculated that one penny lent at the start of the Christian era at 5% simple interest would, after roughly 1,800 years, be worth only about seven shillings — less than a pound. The very same penny at 5% compound interest would be worth more gold than the entire solar system could hold. Same coin, same rate: the only difference is whether interest is allowed to earn interest.
Example problems
- short horizon - Short horizon where simple and compound outcomes remain close.
- long horizon - Long horizon where compounding gap becomes pronounced.
- high rate - Higher rates and time horizon amplify compound outperformance.