Question

In how many rears will a sum of Rs. $800$ at $10\%$ per annum compound interest, compounded semiannually becomes Rs. $926.10$?

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

Answer 1

The correct option is D $1\frac{1}{2}$years

Given, $P=$ Rs. $800,r=10\%$ p.a. $=5\%$ per half year, $A=$ Rs. $926.10$, Time $=2n$
$\therefore 926.10=800{(1+\frac{5}{100})}^{2n}$

$\Rightarrow \frac{9261}{8000}={(1+\frac{1}{20})}^{2n}$

$\Rightarrow {\left(\frac{21}{20}\right)}^3={\left(\frac{21}{20}\right)}^{2n}$
$\Rightarrow 2n=3$

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