Compound interest

Explanation

Simple interest pays you only on the money you put in. Compound interest pays you on the money you put in plus all the interest added so far. Each period, the base grows, so the next period’s interest is a little bigger.

Over short periods the difference is small. Over decades it is dramatic: most of a long-term balance can come from growth on growth rather than from your contributions. That is why starting early matters, and why fees and taxes that skim a little each year have an outsized long-run cost.

How often interest compounds (yearly, monthly, daily) matters a little; the rate and the number of years matter much more. Investment returns are not a fixed interest rate, but the same math applies to average growth. In scenarios, the app compounds balances each period using the return you set (or random returns in a Monte Carlo run).

A handy shortcut is the Rule of 72: divide 72 by the annual rate to estimate the years to double. At 8%, money roughly doubles every 9 years.

Example

You invest $10,000 at 7% a year and leave it alone.

Years	Calculation	Balance
10	$10,000 × 1.07^10	$19,672
20	$10,000 × 1.07^20	$38,697
30	$10,000 × 1.07^30	$76,123

With simple interest at 7%, you would earn $700 a year, or $21,000 over 30 years, ending at $31,000. Compounding adds an extra $45,123.

Compounding frequency: $10,000 at 6% for 10 years compounded yearly gives $10,000 × 1.06^10 = $17,908. Compounded monthly it gives $10,000 × (1 + 0.06/12)^120 = $10,000 × 1.8194 = $18,194, only $286 more.