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.

Answer 1

Given, 

Principal = Rs. 2000 

Rate = 4 % p.a 

C.I = Rs.163.20 

Let time = T years 

So, 

Compound interest \(={P}[({1}+\frac{R}{100})^T-{1}]\)

\(={2000}[({1}+\frac{4}{100})^T-{1}]\) = 163.20

\(={2000}\times(\frac{26}{25})^T-{2000}\) = 163.20

\(={2000}\times(\frac{26}{25})^T\) = 2163.20

\(=(\frac{26}{25})^T\) \(=\frac{2163.20}{2000}\) = \(\frac{676}{625}\)

\((\frac{26}{25})^T\) \(=(\frac{26}{25})^2\)

= T = 2years 

Hence, 

Time = 2 years