What sum of money will amount to ₹ 27783 in one and a half years at 10% per annum compounded half-yearly ?

Let sum of money be ₹ x.

Given,

Time = 1.5 years

Rate = 10% compounded half-yearly

When rate of interest is compounded half-yearly :

By formula,

A = $P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{n \times 2}$

Substituting values we get :

$\Rightarrow 27783 = x \times \Big(1 + \dfrac{10}{2 \times 100}\Big)^{1.5 \times 2} \\[1em] \Rightarrow 27783 = x \times \Big(1 + \dfrac{1}{20}\Big)^3 \\[1em] \Rightarrow 27783 = x \times \Big(\dfrac{21}{20}\Big)^3 \\[1em] \Rightarrow 27783 = \dfrac{9261x}{8000} \\[1em] \Rightarrow x = \dfrac{27783 \times 8000}{9261} \\[1em] \Rightarrow x = ₹ 24000.$

Hence, sum of money = ₹ 24000.