If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Personal finance>Unit 3

Lesson 1: Compound interest basics

# The rule of 72 for compound interest

Using the Rule of 72 to approximate how long it will take for an investment to double at a given interest rate. Created by Sal Khan.

## Want to join the conversation?

• But why 72? I still don't see how that one number (it seems to arbitrary) can be a universal predictor of the doubling problem.
• Since the aim is to double your money, just try to put it as an equation and you will figure out that if you want to double your money(x) and you know the interest rate(y), the duration(n) can be determine by this equation :
x*(1+y/100)^n=2x ==> n= (ln2)/(ln(1+y/100))
since y/100 is close to zero, ln(1+y/100) is close to y/100 so you can approximate the solution to :
n = 100*ln2/y and 100*ln2 is sensibly 70. That's why in the video he said we can use 69 or 70, but 72 is more accurate....
• what if i want to triple or quadruple my money, does 72 work for that too?
• From wikipedia: "Extending the rule of 72 out further, other approximations can be determined for tripling and quadrupling. To estimate the time it would take to triple your money, one can use 114 instead of 72 and, for quadrupling, use 144." https://en.wikipedia.org/wiki/Rule_of_72
• Is there a similar rule for simple interest
• Yes, you just use 100 instead of 72. For example, at 5% annual interest, it would take 20 years to double your money (100 / 5 = 20).
• Based on the spreadsheet, wouldn't 73 be a better working number considering it's in the middle?
• The rule of 72 is more about getting an easy estimate than being perfectly accurate. 72 is commonly used because it has so many divisors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36), so it's much easier to calculate in your head.
• Check algebra 2 if you need help on logarithms.
• Is there a "rule of something" good for approximating continuously compounded growth? Also, is there a way to approximate decay, like with half-lives?
• Sal addresses decay (half lives) in other videos, but I can not remember where. You may have to look over the list. He addressed continuously compounded growth a few videos back.
• Is the relation between the percentage and the time it takes you to double your money linear?
• Nope. It´s kind of logarithmic. In the section Interest and Debt (rule of 72) one of the teachers shows an excel spreadsheet where he graphs it.
• Thank you! It was helpful. But what about trebling or four times & so on? Is there any similar rule?
• LN(2) To doubling 69.31 = ca. 72
LN(3) To Trebling 109.86 = ca. 110
LN(4) To Four times... Etc.
* LN = natural logarithm