The Formula
A = P (1 + r/n)^(nt)
- A = final amount
- P = principal (starting amount)
- r = annual interest rate (decimal)
- n = compounding periods per year
- t = number of years
Common Mistakes
- Forgetting to convert percentage to decimal — using 8 instead of 0.08 inflates the result astronomically.
- Mixing up n and t — n is compounding frequency per year, t is total years, not total periods.
- Ignoring compounding frequency entirely — monthly compounding at 8% earns noticeably more than annual compounding at 8% over long horizons.
Quick Reference
Rule of 72: divide 72 by your interest rate to estimate how many years it takes to double your money. At 8%, that's roughly 9 years — matching our worked example above almost exactly.
Frequently Asked Questions
Why does the rule of 72 work?
It's a mathematical approximation derived from the natural logarithm of 2 divided by the growth rate, and it stays accurate within a percentage point or two for typical interest rates between 6-10%.
Is compound interest only relevant to savings?
No — it applies equally to debt. Credit cards and loans compound against you the same way savings compound for you, which is exactly why high-interest debt grows so dangerously fast if left unpaid.
