Question

At what rate percent compound interest, $Rs800$ amounts to $Rs926.10$ in $1\frac{1}{2}$ years, interest being compounded half yearly?

Answer 1

We have

Principle $=Rs2800$

Amount $=Rs926.10$

Time period $1\&\frac{1}{2}=3$half yearly

Let ${}^{\prime }{R}^{\prime }$ be the rate of interest

Now,

$A=P{\left(1+\frac{R}{100}\right)}^n$

$\Rightarrow 926.10=800{\left(1+\frac{R}{100}\right)}^n$

$\Rightarrow \frac{9261}{8000}={\left(1+\frac{R}{100}\right)}^3$

$\Rightarrow {\left(\frac{21}{20}\right)}^3={\left(1+\frac{R}{100}\right)}^3$

$\Rightarrow \frac{21}{20}=1+\frac{R}{100}\left[cancle3bothside\right]$

$\Rightarrow \frac{21}{20}-1=\frac{R}{100}$

$\Rightarrow \frac{1}{20}=\frac{R}{100}$

$\therefore R=5\%$

Hence, the required interest rate is $5\%$.