Question

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

Answer 1

Let the rate percent per annum be $R$.

Because interest is compounded every six months, $n$ will be $3$ for $1.5$ years.

Now,$A={P(1+\frac{R}{200})}^n$

$2315.25=2000{(1+\frac{R}{200})}^3$

${(1+\frac{R}{200})}^3=\frac{2315.25}{2000}$

${(1+\frac{R}{200})}^3=1.157625$

$(1+\frac{R}{200})3={\left(1.05\right)}^3$

${(1+\frac{R}{200})}^3={\left(1.05\right)}^3$

$\frac{R}{200}=1-1.05=0.05$

$R=200\times 0.05=10$

Thus, the required rate is $10\%$ per annum