The interest on a sum of Rs 2000 is being compounded annually at the rate of 4% per annum.
Question:

The interest on a sum of Rs 2000 is being compounded annually at the rate of 4% per annum. Find the period for which the compound interest is Rs 163.20.

Solution:

Let the time period be $\mathrm{n}$ years.

Then, we have:

$\mathrm{CI}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}-\mathrm{P}$

163. $20=2,000\left(1+\frac{4}{100}\right)^{\mathrm{n}}-2,000$

$2,163.20=2,000(1.04)^{\mathrm{n}}$

$(1.04)^{\mathrm{n}}=\frac{2,163.20}{2,000}$

$(1.04)^{\mathrm{n}}=1.0816$

$(1.04)^{\mathrm{n}}=(1.04)^{2}$

On comparing both the sides, we get:

n = 2

Thus, the required time is two years.