Question

In how many years will a sum of Rs. 800 at 10% per annum compounded, semi-annually become Rs. 926.10 ?

• A. $1\frac{1}{3}$
• B. $1\frac{1}{2}$
• C. $2\frac{1}{3}$
• D. $2\frac{1}{2}$

Answer 1

The correct option is B $1\frac{1}{2}$

Let the time be n years. Then,
$\Rightarrow 800\times {\left(1+\frac{5}{100}\right)}^{2n}=926.10$
$\Rightarrow {(1+\frac{5}{100})}^{2n}=\frac{9261}{8000}$
$\Rightarrow {\left(\frac{21}{20}\right)}^{2n}={\left(\frac{21}{20}\right)}^3$
$\Rightarrow 2n=3$

$\Rightarrow n=\frac{3}{2}$
$\therefore n=1\frac{1}{2}$ years.