Question

What sum will become rupees 9826 in 18 months at 2.5 % interest rate, when the interest is compounded half yearly?

How to do this and is there any way to do this easily without long multiplications?

Answer 1

Suppose the required sum is P.
Time; t = 18 months = $\frac{18}{12}=\frac{3}{2}$ years
Rate of interest; r = 2.5%
Since the interest is compounded half yearly, so number of times interest is compounded; n = 2
So the amount accumulated after the given time is given by;
$$\begin{gathered} A=P{\left(1+\frac{r}{n\times 100}\right)}^{nt} \\ \Rightarrow 9826=P{\left(1+\frac{2.5}{2\times 100}\right)}^{2\times \frac{3}{2}} \\ \Rightarrow 9826=P{\left(\frac{81}{80}\right)}^3 \\ \Rightarrow 9826=\frac{531441P}{512000} \\ \Rightarrow P=\frac{9826\times 512000}{531441}=9466.54 \end{gathered}$$
Therefore the required sum is Rs.9466.54.