The formula

A = P(1 + r/n)nt
  • P what you start with
  • r yearly rate, as a decimal
  • n times per year interest is added
  • t years
  • A what you end with

How often it compounds

$1,000 at 5% for 30 years

  1. Yearly$4,322
  2. Monthly$4,468
  3. Daily$4,481
  4. Continuous$4,482

Yearly to daily adds $159. Time matters far more: the same $1,000 left 60 years becomes $18,679.

Rule of 72

Years to double: 72 ÷ rate vs exact

Rate72 ÷ rExact
2%36 yrs35 yrs
4%18 yrs17.7 yrs
6%12 yrs11.9 yrs
8%9 yrs9 yrs
10%7.2 yrs7.3 yrs
12%6 yrs6.1 yrs

Debt runs the same curve: an unpaid balance at 24% doubles in about 3 years.