The rule of 72 is a great approximation tool for GMAT Math questions involving compounding (e.g., compound interest, bacterial growth rate etc)

Let’s start with an example:

**John has an option of depositing $100 he saved with his friend or with the Bank. His friends, he will give John back 4 times the initial deposit money along with the principal in 10 years. The bank will provide him 12% pa on his deposit compounded annually. What is the closest number of years John would have to leave his money with the Bank to get back a return equivalent to what his friend will provide him?**

**A. 10**

**B. 12**

**C. 13**

**D. 18**

**E. 21**

Readers are encouraged to take some time to tackle the above question 🙂

**Let’s look at the traditional way of solving this question:**

Sum provided by John’s friend at the end of 10 years = 4 x $100 + $100 = $500

**Compound interest returns = (Principal) x (1+ Rate/100) ^{# of years}**

= ($100) x (1 + 12/100)^{# of years}

= $100 x (1.12)^{# of years}

This should equate to return from John’s friend

$100 x (1.12)^{# of years} = $500

1.12^{# of years} = 5

Now, using trial and error and acute mathematical prowess we may be able to figure out # of years. However, this technique is a bit time consuming.

**Here’s is the rule of 72 technique:**

**Trick: The # of years it takes for something to double when compounded at a certain interest rate R is roughly equal to 72/R**

Using the above, at 12% interest rate, it would take approximately 72/12 = 6 years for John’s money to double. Another 6 years and John’s money would become 4 times (i.e, 2 x 2)…a bit more time and we would have 5 times the money (i.e., $500)

In total we have accounted for 6 years + 6 years + a bit more = 12 years + bit more

Looking at the options, this can only be Option (C).

It cannot be Option (D) as John’s money would become 8 times till then (18 years = 3 spans of 6 years each)

So, we go with **Option (C)**

Told you, this was going to be fast 🙂