Usually the interest rate used on deposits (and loans) is in the form of APR, which means that annual is the correct compounding period to use. And with annual, as your spreadsheet shows, 72 is more accurate above 5% and not that shabby below. Further, 72 has more factors and so is easier to use to estimate compounding in your head, which is the whole point.

Y = ln(2) / (n * ln(1 + r/n))

where Y = number of years, n = how often interest compounds in a year (e.g, n=12 for monthly), and r is rate (as a decimal, 5% means r = 0.05). So then, if we want a “rule” to use as an approximate guide, we take that and multiply by the rate (so that when we divide by the rate later, we get the number of years).

I personally always use “Rule of 70″ for my own use, as it tends to be pretty good for typical APR’s and compounding schemes.

Jared, please tell me you used a calculator to do all that and that your head hurt when you were done. If not, you might want to try laying off the algebra before bedtime! Never really thought of it this way though, so thanks!

~bayou

If you move from “continuously” to daily, or weekly, interest accrues slower, so you have to increase the 69.31 upwards. And the adjustment depends on both the rate and the accrual period. For example:
5% daily => Rule of 69.32
20% daily => Rule of 69.33
5% monthly => Rule of 69.46
20% monthly => Rule of 69.89
5% annually => Rule of 71.03
20% annually => Rule of 76.04