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?
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 🙂