Compound interest — the gap that opens when interest earns interest.
Most people internalize the idea, then under-estimate the size of it. Scrub the controls below to feel where the gap goes from boring to absurd.
TL;DR
Simple interest pays only on what you started with. Compound pays on the running total.
The two look nearly identical for the first few years — the gap is almost all in the back half.
Two knobs dominate the outcome: rate and time. Doubling either roughly squares the gap.
The sandbox — drag the knobs.
The dashed line is what your money would do under simple interest; the solid line is what it does under compounding. The shaded area between them is the part you're either earning or paying away, depending on which side of the loan you're on.
Principal grows over time
$32,071 at year 30
· gap of $17,071
What it looks like, with and without.
Without compounding
With compounding
Year 1
$10,400
$10,400
Year 10
$14,000
$14,802
Year 30
$22,000
$32,434
What changed
+$400 / year, forever.
Each year's interest earns interest the next year.
FAQ
Why does the gap stay small for so long?
The first few years compound on almost nothing — the bonus is tiny. The compounding effect is multiplicative, so it only starts to matter when there's a substantial running total to multiply against.
What does "compounding frequency" do?
It moves the curve up a little. Monthly compounding earns a touch more than annual, and continuous compounding is the theoretical ceiling. The slider above assumes annual compounding for clarity.
Does this work the same way on debt?
Exactly the same shape, with the opposite sign. Credit card debt that compounds monthly at 22% APR doubles in about 40 months if you make no payments.
Glossary
Simple interest
Interest paid only on the original principal. The amount earned per period never changes, no matter how long you hold the position.
Compound interest
Interest paid on principal plus previously-earned interest. Each period's earnings become next period's base, which is why the curve bends upward.
Rule of 72
A back-of-envelope shortcut: 72 ÷ rate ≈ years to double. At 6%, money doubles in about 12 years; at 9%, about 8.