Question

Find the difference between simple interest and compound interest on ₹20000 at 8 p.c.p.a.

Answer 1

Disclaimer: In the question "Time" is not given. So the question is solved taking time as 2 years, because simple interest and compound interest will be same for one year.

Here, P = Principal = ₹ 20000
R = 8 %
N = 2 years

$$\begin{gathered} \mathrm{Simple}\mathrm{interest}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{N}}{100} \\ =\frac{20000\times 8\times 2}{100} \\ =3200 \\ \mathrm{Amount}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}} \\ =20000{\left(1+\frac{8}{100}\right)}^2 \\ =20000{\left(1+\frac{2}{25}\right)}^2 \\ =20000{\left(\frac{27}{25}\right)}^2 \\ =23328 \\ \mathrm{Compound}\mathrm{interest}=23328-20000 \\ =3328 \\ \mathrm{Compound}\mathrm{interest}-\mathrm{Simple}\mathrm{interest}=3328-3000 \\ =128 \end{gathered}$$

Hence, the difference between simple interest and compound interest is ₹ 128.