Question

A principal of Rs 25000 when invested for 6 months at certain rate compounded quarterly gives Rs 26010. What is the rate of interest?

Answer 1

Suppose the rate of interest is R%.
Here, Principal amount; P = Rs.25000
Time; T = 6 months = $\frac{6}{12}=\frac{1}{2}\mathrm{year}$
Since the interest is compounded quarterly, so number of times interest is compounded; n = 4
So; amount accumulated after 6 months is given by;
$$\begin{gathered} A=P{\left(1+\frac{R}{n\times 100}\right)}^{nT} \\ \Rightarrow 26010=25000{\left(1+\frac{R}{400}\right)}^{4\times \frac{1}{2}} \\ \Rightarrow 26010=25000{\left(1+\frac{R}{400}\right)}^2 \\ \Rightarrow {\left(1+\frac{R}{400}\right)}^2=\frac{26010}{25000} \\ \Rightarrow {\left(1+\frac{R}{400}\right)}^2=1.0404 \\ \Rightarrow {\left(1+\frac{R}{400}\right)}^2={\left(1.02\right)}^2 \\ \Rightarrow 1+\frac{R}{400}=1.02 \\ \Rightarrow \frac{R}{400}=.02 \\ \Rightarrow R=400\times .02=8 \end{gathered}$$
Therefore rate of interest is 8% per annum.