The rule of 72 for compound interest | Interest and debt | Finance & Capital Markets | Khan Academy

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.

Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head.

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[toothpickvideos]

I'm totally watching all these videos 3 hours before my finals... I am starting to finally grasp the idea finally. Thanks!

[alxjones]

You can show that 72 is a good approximation by looking at what number y satisfies the relationship log(2)/log(1+x) = y/100x, where x is the decimal representation of the percentage. Solving this gives y=100log(2)x/log(1+x), and restricting x values to reasonable interest rates, 0<x<.2, we can see roughly that 69<y<76. If you take the very middle of this range you get 72.5, so we could use 72 or 73 and get pretty close for reasonable values of x.

[MsScruffy]

The rule of 69 is probably more fun when using logs.
But complexity aside -- if simple interest means it takes 10 years to double $100 at 10%.
And now we know the rule of 72 -- then it takes 7.2 years to double with compound interest. IT is that simple.

10 years at simple interest to double
7.2 years at compound interest

NOW i can do it in my head and approximate other interest values. So why all the
COMPLEXITY. ???

[effortless]

It works with both. ln(2)/ln(1.1) = 0.693/0.0953 = 7.27

You just need to use the same base for the numerator and the denominator.
Sal hints at this at 4:23 when he says "x should equal to log base anything really 2..."

[karhukivi]

It's actually the "Rule of 69" but using 70 or 72 makes the calculation easier with some loss of accuracy. This is continuous compounding but banks etc. might apply less frequent compounding periods such as months or years. Handy as a quick mental arithmetic method - it is a consequence of exponential growth as ln(2) = 0.69315... or 69% approx.

[GIJew]

No, the rule of 69 has nothing to do with math, lad.

[XXX-szlt]

It is difficult to figure out which the next video is, related to previous. Could you please arrange them in order?

[Melthornal]

Log. ln is a natural log, which is base e. Log is base 10. You want log for this.

[mrbeakus]

I Just wanted help on year 10 maths it all got hard

[matthewwon]

So does the rule of 72 only apply when it's doubling the amount? It doesn't work if it's triple or quadruple?

[jriver]

can you use this rule to estimate how long it will take investments to double with interest compounded semi-annual or quarterly ?

[ghada]

It's cute how he really wanted to do just another one "for fun" °=°

[nleinen]

what would you do for tripling or continuously compounding?

[amazingnessforever]

True or False: hypothetically if you made a ridiculous amount of profit on your investment it could be more beneficial for you to invest in a regular capital investment over an Ira being that the taxes on the capital investment are only 15 % as opposed to 25% when you are retired

[mookiecookie]

Interesting stuff, but doing the actual math really is not that much harder. I suppose if you have to do everything in your head this makes sense, but I don't know when you would need to make any sort of financial decision/calculation without access to a calculator (you can do all calculations necessary in the calculator app on your phone).

[yathishification]

If i invest 5000 per month for 10years and annual return would be 8%, how much i will be getting at the end of policy term ?

[alexzandercastillo]

Could this work for continuous too or simply just annual

[attackhelicopter]

I was actually guessing it would be around 8 before you used the calculator . I feel kinda smarts :)

[Prebest]

What the 72 suppose to be the input money?

[JannCristobal]

what happens when the compounding period is changed to monthly for example, will the percentage change or not?