Why the curve bends upward
Compound growth has a shape: flat, then gently rising, then steep. The reason is that interest starts earning its own interest. In the early years, your deposits do the heavy lifting; in the later years, growth takes over. Run 20+ year horizons in the table above and find the crossover — the year cumulative interest overtakes cumulative contributions. For a $500/month saver at 7%, that happens around year 17–18. After that point, the account earns more each year than you put in.
The formula (and what actually matters)
P is the starting amount, PMT the periodic deposit, r the annual rate, n compounds per year, t years. But don't let the algebra obscure the hierarchy of what moves the result:
- Time (t) — exponential. It's in the exponent. Ten extra years does more than doubling your deposit ever will.
- Rate (r) — exponential, but mostly out of your hands. The market pays what it pays; your controllable rate lever is minimizing fees and taxes.
- Contributions (PMT) — linear, and fully in your hands. The dial to turn when you can't add years.
- Frequency (n) — nearly irrelevant. Monthly vs. annual compounding changes the outcome by roughly 1% over a decade.
Three honest scenarios
| Saver | Inputs | Balance at 65 (7%/yr) |
|---|---|---|
| Early starter | $300/mo from age 25 (40 years) | ~$787,000 |
| Doubled, but late | $600/mo from age 35 (30 years) | ~$732,000 |
| Lump + steady | $50,000 at 35, plus $500/mo | ~$1,016,000 |
Numbers are nominal, monthly compounding. Read the first two rows again: the late starter contributes $72,000 more out of pocket ($216k vs $144k) and still ends up behind. The calendar is the strongest force in the table — which is why 401(k) contributions in your 20s and 30s punch far above their weight.
Compounding works against you too
The same math runs in reverse on debt. A credit card at 22% APR compounds monthly against you — that's a doubling time of about 3.3 years on an unpaid balance. It's why paying down high-rate debt is often the best "investment" available (see the credit card payoff calculator), and why inflation quietly halves uninvested cash every generation. The Rule of 72 cuts both ways: at 3% inflation, the purchasing power of cash under a mattress halves in ~24 years.