Question

Find compound interest paid when a sum of 30000 is invested for 2 years and three months at 8.5%p.a compounded annually?

Answer 1

Principal amount; P = Rs.30000
Time; t = 2 years 3 months = $2\frac{3}{12}=2\frac{1}{4}=\frac{9}{4}\mathrm{years}$
Rate of interest; r = 8.5% p.a.
So, amount accumulated after 2 years 3 months is given by;
$$\begin{gathered} A=P{\left(1+\frac{r}{100\times n}\right)}^{nt} \\ =30000{\left(1+\frac{8.5}{100}\right)}^{\frac{9}{4}}\{\mathrm{since}\mathrm{the}\mathrm{interest}\mathrm{is}\mathrm{compounded}\mathrm{annually}\mathrm{so}n=1\} \\ =30000{\left(\frac{108.5}{100}\right)}^{\frac{9}{4}} \\ =30000{\left(1.085\right)}^{\frac{9}{4}} \\ =30000\times 1.20 \\ =36000 \end{gathered}$$
therefore compound interest = Rs.36000 - Rs.30000 = Rs.6000