The formula, and what each piece does
A lump sum grows by the rate r each period, compounded over n periods. The exponent is what makes it powerful: interest earns interest. If you also pay in regular contributions, each one grows for the time it has left, and that total is added to the lump-sum result.
What $10,000 becomes
| Rate | 10 years | 20 years | 30 years |
|---|---|---|---|
| 3% | $13,439 | $18,061 | $24,273 |
| 5% | $16,289 | $26,533 | $43,219 |
| 7% | $19,672 | $38,697 | $76,123 |
| 10% | $25,937 | $67,275 | $174,494 |
Lump sum only, compounded yearly, no extra deposits. Small gaps in the rate widen enormously over time: at 30 years, 7% ends up more than three times what 3% does.
Doubling time, in your head
To see how fast money grows, divide 72 by the return. The answer is roughly the number of years to double.
- 3% → 24 years. Safe savings barely keep pace with inflation.
- 6% → 12 years. A balanced portfolio doubles about twice in a working career.
- 8% → 9 years. A long-run stock-market average; four doublings in 36 years is a 16x gain.
What the number leaves out
Future value is a projection, not a promise. Two things quietly shrink it.
- Inflation. $100,000 in 30 years at 3% inflation buys about what $41,000 does today. Subtract expected inflation from the rate to see real growth.
- Tax and fees. A 6% gross return can net 3–4% after tax and fund costs, which roughly doubles the doubling time.
Common questions
What is the future value formula?
For a lump sum, future value equals present value times (1 plus the rate) raised to the number of periods: FV = PV x (1 + r)^n. If you also add regular deposits, their growth is added on top.
How long does it take to double my money?
Divide 72 by the yearly return percentage. At 6% it takes about 12 years, at 8% about 9 years. The Rule of 72 is accurate for rates in the 6 to 10% range.
Does compounding more often make a big difference?
Only a small one. On $1,000 at 5% for a year, annual compounding gives $1,050.00 and daily gives $1,051.27 — about a dollar. The rate and the time horizon matter far more than the frequency.
