Question

The compound interest on Rs. 1800 at $10\%$ per annum for a certain period of time is Rs. 378. Find the time in years.

Answer 1

Principal (P) = Rs. 1800
C.I = Rs. 378
$\therefore$ Amount (A) = P + C.I = Rs. 1800 + 378
= Rs. 2178
Rate (R) $=10\%$ p.a
Let n be the period in years
$\because A=P{(1+\frac{R}{100})}^n\Rightarrow \frac{A}{P}={(1+\frac{R}{100})}^n$
$\Rightarrow Rs.\frac{2178}{1800}={(1+\frac{10}{100})}^n$
$\Rightarrow Rs.\frac{121}{100}={\left(\frac{11}{10}\right)}^n\Rightarrow {\left(\frac{11}{10}\right)}^2={\left(\frac{11}{10}\right)}^n$
Comparing, we get
n = 2
$\therefore$ Period = 2 years.