Snowballr · Cheat sheet
Compound interest cheat sheet
The formula, the four levers, and the numbers that show why time beats rate.
For: Beginners and educators · Source: snowballr.io/cheat-sheets/compound-interest
Teaching this topic? Try the printable classroom lesson and student worksheet.
The formula
A = P × (1 + r/n)^(n × t) + PMT × [((1 + r/n)^(n × t) − 1) / (r/n)]
A = future balance · P = principal · r = annual rate (decimal) · n = compounds per year · t = years · PMT = periodic contribution.
Rule of 72 (doubling time)
Years to double ≈ 72 / annual return %.
- 6% → ~12 years
- 7% → ~10.3 years
- 8% → 9 years
- 10% → 7.2 years
The four levers (ranked by impact)
- TIME — exponent in the formula, biggest lever
- RATE — base of the exponent, second biggest
- CONTRIBUTION — linear; doubles output if doubled
- PRINCIPAL — linear; matters less than people think
Reference scenarios at 7% nominal (month-end deposits)
| Monthly | Years | Final balance | Total contributed | Growth |
|---|---|---|---|---|
| $100 | 30 | $121,997 | $36,000 | $85,997 |
| $500 | 30 | $609,985 | $180,000 | $429,985 |
| $500 | 40 | $1,312,407 | $240,000 | $1,072,407 |
| $1,000 | 30 | $1,219,971 | $360,000 | $859,971 |
| $1,000 | 40 | $2,624,813 | $480,000 | $2,144,813 |
Decision rules
- Starting later costs more than contributing less. Start.
- A 1% expense ratio costs ~28% of final balance over 30 years vs a 0.05% fund.
- Compounding frequency is a rounding error vs time and rate.
- Inflation roughly halves your real return — model nominal AND real.