Question

Ishita invested a sum of Rs. 12000 at $5\%$ per annum compound interest. She received an amount of Rs. 13230 after n years. Find the value of n.

Answer 1

Principal (P) = Rs. 12000
Amount (A) = Rs. 13230
Rate (R) $=5\%$ p.a
Period = n years
$\therefore$ Amount $=P{(1+\frac{R}{100})}^n$
$\Rightarrow Rs.13230=Rs.12000{(1+\frac{5}{100})}^n$
$\Rightarrow Rs.\frac{13230}{12000}={\left(\frac{21}{20}\right)}^n$
$=Rs.\frac{441}{400}={\left(\frac{21}{20}\right)}^n\Rightarrow {\left(\frac{21}{20}\right)}^2={\left(\frac{21}{20}\right)}^n$ (Dividing by 30)
Comparing, we get
n = 2