$10,000 at 7% for 30 years. Simple interest pays you $21,000 in gains. Compound interest pays you $66,000. Same principal, same rate, same time — 3× the outcome from a single setting.
The two formulas
- Simple:
total = principal × (1 + rate × years). $10,000 × (1 + 0.07 × 30) = $31,000 total, $21,000 gain. - Compound:
total = principal × (1 + rate)^years. $10,000 × 1.07^30 = $76,123 total, $66,123 gain.
Year-by-year (7% rate)
- Year 1 — Simple: $10,700. Compound: $10,700. Identical.
- Year 5 — Simple: $13,500. Compound: $14,026. Small gap.
- Year 10 — Simple: $17,000. Compound: $19,672. Gap widens.
- Year 20 — Simple: $24,000. Compound: $38,697. Compound now 61% ahead.
- Year 30 — Simple: $31,000. Compound: $76,123. Compound now 2.5× simple.
- Year 40 — Simple: $38,000. Compound: $149,745. Nearly 4×.
Why reinvestment is the whole game
The difference between simple and compound is reinvestment. Every dollar of interest left in the account next year earns interest on itself. Every dollar withdrawn breaks the chain and drops you back onto the simple curve. Index funds, DRIP plans, and 401(k)s all default to reinvestment for exactly this reason.
The other side of the coin
The same math runs against you with credit card debt. 24% APR on a balance you don’t pay off becomes a geometric series that can easily cost more in interest than the original purchase. Reinvestment working against you is called a debt spiral.
Enter principal, monthly contribution, rate, years. Full compound interest projection with yearly breakdown.