What is compound interest, in one sentence?
Compound interest is interest earned on your interest: each period's earnings are added to the balance, so the next period earns on a bigger amount, and growth speeds up the longer you leave the money alone.
The compound interest formula
For a single deposit:
A = P × (1 + r/n)n×t
- A: the final amount
- P: the starting amount (principal)
- r: the yearly rate as a decimal (7% = 0.07)
- n: compounding periods per year (12 for monthly)
- t: years
With a regular monthly deposit (PMT), add PMT × ((1 + r/n)n×t − 1) ÷ (r/n). The game uses exactly this: monthly compounding, with deposits at the end of each month.
Early and small beats late and big
Two savers each deposit $96,000 in total at 7% a year. The early saver puts in $200 a month for 40 years and ends with about $524,963. The late saver puts in twice as much, $400 a month, but only for 20 years, and ends with about $208,371. Same deposits, roughly 2.5 times the money, purely from time. That is the instinct the game trains.
Rule of 72: how fast money doubles
Divide 72 by the yearly rate for a quick estimate of the years it takes money to double.
| Yearly rate | Rule of 72 estimate | Exact (yearly compounding) |
|---|---|---|
| 2% | 36.0 years | 35.0 years |
| 3% | 24.0 years | 23.4 years |
| 4% | 18.0 years | 17.7 years |
| 5% | 14.4 years | 14.2 years |
| 6% | 12.0 years | 11.9 years |
| 7% | 10.3 years | 10.2 years |
| 8% | 9.0 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6.0 years | 6.1 years |
Tips for a long streak
- Years matter most. Ten extra years at the same rate often beats a much bigger starting balance.
- Rate matters next: 10% for 30 years is about 17 times the money; 5% for 30 years is about 4.5 times.
- Monthly deposits add up fast. $500 a month is $6,000 a year before any growth.
- When two plans look close, estimate each with the Rule of 72 and count the doublings.
More free money games
For learning and fun only. PuzzlePage's games explain general concepts and are not financial, tax, insurance or legal advice. Rules vary by state and country and change over time; for decisions about your own situation, talk to a licensed professional. Real investments do not earn a fixed rate; returns vary and can be negative.