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

Given:

Principal (P) = ₹1,200

Amount (A) = ₹1,348.32

Rate of interest (R) = 6% per annum

Formula Used:

Compound Interest Formula: A = P \((1 + \frac{R}{100})^n\)

Calculation:

We need to find the number of months (n).

Given:

₹1,348.32 = ₹1,200 \((1 + \frac{6}{100} )^\frac{n}{12}\)

⇒ 1.1236 = \((1.06)^\frac{n}{12}\)

Taking natural logarithm on both sides:

\(ln(1.1236) = \frac{n}{12} × ln(1.06)\)

⇒ \(\frac{n}{12} = ln(1.1236) / ln(1.06)\)

⇒ \(\frac{n}{12} = 0.1167 / 0.0583\)

⇒ \(\frac{n}{12} = 2\)

⇒ n = 2 × 12

⇒ n = 24

Hence, the number of months required is 24 months.