Question

In how much time will a sum of Rs. 1600 amount to Rs. 1852.20 at $5\%$ per annum compound interest?

Answer 1

Principal (P) = Rs. 1600
Amount (A) = Rs. 1852.20
Rate (R) $=5\%$ p.a
Let n be the time
$\because A=P{(1+\frac{R}{100})}^n$
$\frac{A}{P}={(1+\frac{R}{100})}^n$
$\Rightarrow Rs.\frac{1852.20}{1600}={(1+\frac{5}{100})}^n$
$\Rightarrow Rs.\frac{185220}{100\times 1600}={\left(\frac{21}{20}\right)}^n$
$\Rightarrow Rs.\frac{9261}{8000}={\left(\frac{21}{20}\right)}^n$
$\Rightarrow {\left(\frac{21}{20}\right)}^3={\left(\frac{21}{20}\right)}^n$
Comparing, we get
n = 3
$\therefore$ Period = 3 years.