# Rule of 72

The writer is a Delhi, India based Certified Financial Planner CFPCM, conferred upon by the
Financial Planning Standards Board. If you are an Indian resident looking for a financial plan prepared according to your needs & goals, write to her at shruti(AT)richesawait.com Every investor (or future investor) wants to know “How quickly will my money grow?” or “I want a certain amount of money in the next 6 years, where should I invest?” or “How long should I stay invested to double my initial investment?”

But to get these answers you either have to solve complicated math equations or rely completely on promotional material of the investment product. Right? Well not really, you can find the answers to these questions quickly and easily with the help of the Rule of 72.

Rule of 72 is a shortcut for a compounding formula, and it helps in finding out how much time it will take to double your money, provided you stay invested and reinvest your interests/gains.

# $T=\displaystyle \frac{72}{R}$

where T = time in years to double the investment and R = compounded annual rate of interest.

So, according to the rule of 72, all you have to do is divide 72 with the rate of interest and you will get the approximate number of years in which your money will double.
For example: if you invest 5,000 at 6% p.a. and stay invested your money will double to 10,000 in 12 years using T=72/R where R = 6.

The actual formula would be $T=\frac{ln(2)}{ln(1+r/100)}$
where ln(2) is the natural logarithm of 2 which is approx. 0.693.
And calculating ln(1+0.06) we get 0.0582. So, T = 0.693/0.0582 which is 11.9

It’s not easy to remember the real formula, is it? You can’t even calculate that stuff using a regular calculator.

But the 72 workaround works just fine. You’ll notice that we didn’t go with 69 which would be a natural choice since ln(2) is approximately 0.69. This is because 72 is divisible by 2, 3, 4, 6, 8, 9, and 12 making it very easy for calculations.

You can also find out what interest rate you should invest your money to make it double in a desirable number of years.
For example: if you have say ₹1 lakh and want to double this to ₹2 lakhs in the next 6 years. You have to invest ₹1 lakh today in an investment vehicle giving a rate of interest @ 12% using R=72/T  where T = 6 years.

Rule of 72 is based on a rate of interest compounded annually and time, invested amount is not a factor at all. Whatever the amount is, it will take the same number of years to double the said amount.

Uses of the Rule of 72:

• Helps in comparing different investment vehicles: Let’s understand this with the help of an example. Suppose you have ₹2 lakhs with you and want to invest the same, but are not sure where. Now let’s see your options –
1. Savings Bank Account @ 4%: your money will double in 18 years (T=72/4).
2. Fixed Deposit @ 6%: your money will double in 12 years (T=72/6).
3. Debt Mutual Fund @ 9%: your money will double in 8 years (T=72/9).

Therefore with the help of Rule of 72, you can see that if you deposit ₹2 lakhs in savings account you’ll have ₹4 lakhs in 18 years. But if you invest the same in Debt mutual fund you’ll have ₹4 lakhs in 8 years.

• Warns you against scammy investment schemes: If you come across a scheme which guarantees to double your invested money in 1 year, with the help of Rule of 72 you can easily realize that they are offering a return of 72% p.a. (R=72/1). Now, this kind of guaranteed return in such a short time is almost impossible. Hence, you can easily discard the scheme as nothing but a scam.

Things to keep in mind while applying the rule of 72:

1. This rule assumes that you are going to stay invested for compounding to take place. If you withdraw from your investment the results will be different.
2. Rule of 72 is a shortcut of a complex compound formula. Therefore, the answers are close estimates but not exact.
3. It takes only return into consideration while computing the answer. It ignores other factors like inflation and taxation etc.
4. Rule of 72 may not work in cases where the rate of return keeps changing, like in equity because returns are changing based on the market condition.

If you want to find out how many years it will take to triple your initial investment use T=114/R. 🙂