Question

Find the rate percent per annum, if Rs. 2000 amount to Rs. 2315.25, in an year and a half, interest being compounded six monthly.

Answer 1

Principal (P) = Rs. 2000
Amount (A) = Rs. 2315.25
Period (n) $=1\frac{1}{2}$ years or 3 half-years.
Let R be a rate of half yearly, then
$\frac{A}{P}={(1+\frac{R}{100})}^n$
$\Rightarrow \frac{2315.25}{2000}={(1+\frac{R}{100})}^3$
$\frac{231525}{100\times 2000}={(1+\frac{R}{100})}^3$
$\Rightarrow \frac{231525}{100\times 2000}={(1+\frac{R}{100})}^3$
$\Rightarrow \frac{9261}{8000}={(1+\frac{R}{100})}^3$ (Dividing by 25)
$\Rightarrow {\left(\frac{21}{20}\right)}^3={(1+\frac{R}{100})}^3$
Comparing both sides, we get
$1+\frac{R}{100}=\frac{21}{20}=1+\frac{1}{20}$
$\therefore \frac{R}{100}=\frac{1}{20}\Rightarrow R=\frac{100}{20}=5$
$\therefore$ Rate $=5\%$ half yearly or $10\%$ p.a.