Compound annual growth rate smooths a bumpy holding period into one number: the steady yearly rate that would have gotten you from what you put in to what you ended up with.
Three things: what you put in, how long you held it, and what it was worth when you looked again.
Divide ending value by initial investment to get the total growth multiple: ending ÷ initial
Measure the holding period in years, including fractional years for partial-year stretches: (end date − start date) ÷ 365.25
Take that multiple to the power of one over the years, then subtract one: multiple^(1/years) − 1
Same math as above, run backwards: hold your money at a fixed annual rate long enough, and it doubles. Here's how long that takes at a few common rates.
| Growth rate | Years to double |
|---|---|
| 3% | 23.4yrs |
| 5% | 14.2yrs |
| 8% | 9.0yrs |
| 10% | 7.3yrs |
| 12% | 6.1yrs |
| 15% | 5.0yrs |
| 25% | 3.1yrs |