[feoren]

> (for those who don't know too, percentages are reversible so at 10% you double your money every 7 years...)

That is not true at all. "Percentages are reversible" means that 30% of 50 is the same as 50% of 30, so 15. It does not mean that anywhere you see a percent related to another number, you can just switch them around.

Easy counterexamples:

At 100% annual interest, you double your money every 1 year. At 1% annual interest, you double your money every 70 years.

At 41% annual interest, you double your money every 2 years. At 2% annual interest, you double your money every 35 years.

[jessetemp]

It's not perfect, but pretty close if you compound monthly. It works with your examples too.

100% interest (compounded monthly) doubles at about 0.75 years, and 0.75 interest doubles at around 100 years.

41% interest doubles at around 1.75 years, and 1.75 interest doubles at around 41 years

[feoren]

Compounded monthly? That's rather cherry-picked. 0.75% interest compounded monthly doubles in 93 years, not 100. You're compounding the left side differently than the right side.

When talking about stock market returns, people are talking about year-over-year returns. There is no "compounded monthly"; 41% interest "compounded monthly" is actually 49.7% interest. Everyone would call that 49.7%, except credit card commercials that are trying to trick you.

The point is that GP presented the %-switching thing like a rule, but it's not. They've confused how that rule is applied.

Edit: I tried compounding every second. The rule works exactly. e is just such a magic number that continuous compounding is exactly the point at which this rule becomes true. So the more often you compound, the better this rule is. Wild. I still don't recommend using it for annual percentages.