Question

Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in $1\frac{1}{2}$ years, interest being compounded half-yearly?

Answer 1

Principal (P) = Rs. 2000
Amount (A) = Rs. 2662
Rate (R) $=10\%$ p.a
Period (n) $=1\frac{1}{2}$ years or 3 half-years
Let R be the rate of interest half-yearly, then
$\frac{A}{P}={(1+\frac{R}{100})}^n\Rightarrow \frac{2662}{2000}={(1+\frac{R}{100})}^3$
$\Rightarrow \frac{1331}{1000}={(1+\frac{R}{100})}^3$
$\Rightarrow {\left(\frac{11}{10}\right)}^3={(1+\frac{R}{100})}^3$
Comparing, we get
$1+\frac{R}{100}=\frac{11}{10}\Rightarrow 1+\frac{R}{100}=1+\frac{1}{10}$
$\therefore$ Rate $=10\%$ half yearly or $20\%$ p.a