What is Rule of 72 for Investment and how to apply it.

What is Rule of 72 for Investment.

Rule 72 as an investment strategy.

If you are trading in markets your average gains in years is around only 7 to 7.5 %. So, you can use rule 72 to invest in other instruments like ppf and fixed deposits to get the same % of interest , from your recurring deposits, savings accounts, or any safe investment instrument also.

You can double or even triple your money and know when that is going to happen by using rule of 72. So, go ahead and try.

Have you always wanted to be able to do compound interest problems in your head? Perhaps not... but it's a very useful skill to have because it gives you a lightning fast benchmark to determine how good (or not so well) a potential investment is likely to be.

The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years.
(We're assuming the is annually compounded)

As you can see, the "rule" is remarkably accurate, as long as the interest rate is less than about twenty percent; at higher rates the error starts to become significant.

You can also run it backwards: if you want to double your money in six years, just divide 6 into 72 to find that it will require an interest rate of about 12 percent.
Y   =   72 / r   and   r   =   72 / Y

Where, Y and r are the years and interest rate, respectively.

Compound Interest Curve

Suppose you invest Rs.100 at a compound interest rate of 10%. The rule of 72 tells you that your money will double every seven years, approximately:

Years Balance
Now if your Rs. 100
In 7 years = Rs.200 (doubles every seven years)
In 14 years = Rs. 400
In 21 years = Rs. 800

If you graph these points, you start to see the familiar compound interest curve. Try yourself on a paper.

Practice using the Rule of 72
It's good to practice with the rule of 72 to get an intuitive feeling for the way compound interest works. So...

The Rule of 72 - Why it Works

The rule of 72 applies to annually compounded interest, but it's easiest to understand by looking at the case of continuously compounded interest first. We'll write P for the starting principal and r for the return rate (as a decimal); we're looking for Y to double P:

2P = PeYr

Solve for Y:

Y = ln(2) / r

The log of 2 is about equal to .69, so

Y = .69 / r

You can think of this as The Rule of 69 (multiplying the .69 by one hundred, so that the interest rate can be expressed as a percent instead of a decimal). It isn't an estimate - it's the exact answer for doubling your money, assuming that the interest is compounded continuously. It's valid for any value of r.
           
Solving the formula for annually compounded interest is messier:

2P = P(1 + r)Y
Y = ln(2) / ln(1 + r)

We want to approximate this as a neat fraction again,

Y = K / r

where K is some number that will make the approximation pretty good for some ranges of r (and pretty lousy for others). We'll choose K to make the approximation work for a return rate of ten percent:

ln(2) / ln(1 + r) = K / r
ln(2) / ln(1 + .1) = K / 0.1

K = [ln(2) / ln(1.1)] x 0.1

K = .727

Now 72.7 is really closer to 73 than 72, so why isn't it The Rule of 73? Well... uh, the continuously compounded case gives you 69, so you want to round the 72.7 down instead of up... um, plus, 72 is easier to work with, since it's divisible by 12... Anyway, it's only an estimate. So, 72 it is!

Incidentally, if you repeat the above analysis for 8% instead of 10%, you do get a K that rounds to 72 instead of 73:


Interest Rate:  x  %

Resulting Rule  will be
K x 100: 

Guess it guys!