Question

What sum will become ₹9826 in 18 months if the rate of interest is $2\frac{1}{2}\%$ per annum and the interest is compounded half-yearly?
(3 marks)

Answer 1

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

We have,

Principal = P, Amount = ₹9826, $R=2\frac{1}{2}\%$ per annum, and n = 18 months $=\frac{18}{12}years=\frac{3}{2}years$
(1 mark)

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

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

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

$\Rightarrow 9826=P{\left(\frac{81}{80}\right)}^3\Rightarrow P=9826\times {\left(\frac{80}{81}\right)}^3=₹9466.54$

Hence, the required sum = ₹9466.54
(2 marks)