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? [4 MARKS]

Answer 1

Formula : 1 Mark
​Application : 1 Mark
Calculation : 2 Marks

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 $=\frac{18}{12}years=\frac{3}{2}years$

$\therefore A=P{(1+\frac{R}{200})}^{2n}$

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

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

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

Hence, required sum = Rs 9466.54