The mechanism, in one sentence
Interest is added to the balance, and the next round of interest is computed on the larger balance, growth feeding growth. Everything else about compounding is arithmetic detail; this loop is the whole engine, and it is why the yearly table below the calculator curves upward instead of climbing in a straight line.
What the curve actually looks like
$10,000 with $100/month at 8%, compounded monthly:
| Year | Balance | Growth that year |
|---|---|---|
| 5 | $22,246 | $1,654 |
| 10 | $40,491 | $3,053 |
| 20 | $108,170 | $8,240 |
| 30 | $258,393 | $19,752 |
By year 30, one year's growth exceeds the original $10,000, the balance now out-earns its founder. Note also what the totals say: $46,000 was contributed; $212,000 of the final figure is compounding. Time in, not amount in, did the heavy lifting.
The three inputs, ranked by power
- Time. Non-negotiable and non-recoverable. Starting the $100/month at 25 instead of 35 roughly doubles the age-60 outcome. Nothing else in finance offers that trade.
- Rate. 8% vs 6% on the example above is $258,393 vs $160,677 at year 30. Worth pursuing, through low fees above all, since a 1% fee is precisely a 1% rate cut wearing a suit.
- Contributions. The lever fully under your control, and the dominant one over horizons under ~10 years, where compounding has not yet had room to work. See the savings goal calculator for short-horizon planning.
Compounding's evil twin
The identical mathematics runs in reverse on debts, a credit card at 24% is compounding aimed at you, and it out-runs any savings account you own. That asymmetry sets the order of operations: high-rate debt first (debt payoff calculator), then compounding for yourself. Inflation is the quieter twin, compounding prices at ~4–6% against your cash, the inflation calculator shows what that does to uninvested money, and why "safe" cash over decades is not safe at all. For the annualised rate an existing investment actually achieved, use the CAGR calculator.