In how many months, at a rate of 6% compound interest per annum, will a sum of ₹1,200 become ₹1,348.32?

Correct option is C

Given:

Principal (P) = ₹1,200

Amount (A) = ₹1,348.32

Rate = 6% per annum 
We are to find time in months

Formula Used: 

Compound interest formula:

A = $$P \left(1 + \frac{r}{100}\right)^n$$​​

Solution:

A = 1348.32,P = 1200,  r = 6%,  n = number of years

Now, 

​$$1348.32 = 1200 \left(1 + \frac{6}{100}\right)^n \\ \ \\1348.32 = 1200 \left(\frac{106}{100}\right)^n\\ \ \\\frac{134832}{120000} = \left(\frac{53}{50}\right)^n\\ \ \\\frac{2809}{2500}= \left(\frac{53}{50}\right)^n \\ \ \\\left(\frac{53}{50}\right)^2 = \left(\frac{53}{50}\right)^n \\ \ \\\implies n = 2$$​​

So, number of months = 2 × 12 = 24 months