Question

What sum will become Rs 9826 in 18 months if the rate of interest is $2\frac{1}{2}\%$ per annum and the interest is compounded half-yearly?
$\left[3Marks\right]$

Answer 1

Let the required sum i.e. the principal, be Rs P.

We have,

Principal = P, Amount = Rs 9826, $R=2\frac{1}{2}\%$ per annum

and, n = 18 months $=\frac{18}{12}years=\frac{3}{2}years$

$\therefore A=P{(1+\frac{R}{200})}^{2n}$
$\left[1Mark\right]$

$\Rightarrow 9826=P{(1+\frac{\frac{5}{2}}{200})}^{2\times \frac{3}{2}}$

$\Rightarrow 9826=P{(1+\frac{1}{80})}^3$

$\Rightarrow 9826=P{\left(\frac{81}{80}\right)}^3\Rightarrow P=9826\times {\left(\frac{80}{81}\right)}^3=Rs9466.54$

Hence, required sum = Rs 9466.54

$\left[2Marks\right]$