Question

The $CI$ on $\ge 50,000$ invested for one year,when interest is compounded half-yearly at $10$ $\%$ $p.a$ is

• A. $Rs.$ $5000$
• B. $Rs.$ $5125$
• C. $Rs.$ $6000$
• D. $Rs.$ $5500$

Answer 1

The correct option is B $Rs.$ $5125$

Consider the problem

$p=50,000$

$t=1year=2halfyears$

$r=\frac{10}{2}=5\%$ per half year

$\begin{array}{c}A=p{\left[1+\frac{r}{100}\right]}^n\\ =50,000{\left[1+\frac{5}{100}\right]}^2\\ =50,000{\left[\frac{21}{20}\right]}^2\\ =\frac{50,000\times 21\times 21}{20\times 20}\\ =125\times 441\\ =55125\end{array}$

$C.I=A-p$

$=55125-50,000$

$=5125$

Hence, Option $B$ is the correct answer.