Question

Find the rate at which a sum of money will become four times the original amount in 2 years, if the interest is compounded half-yearly.

Answer 1

Given, 

Time = 2 years = 2×2 = 4 half years 

Let rate = R % per annum \(=\frac{R}{2}\text%\) half yearly

Let principal = P 

Amount becomes = 4P 

So,

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

\(={P}[({1}+\frac{R}{2\times100})^4\) = 4P

\(={1}+\frac{R}{200}\) \(={4}^{\frac{1}{4}}\)= 1.4142

\(=\frac{R}{200} = 1.4142-1\)  = 0.4142

= R = \({0.4142\times200}\) = 82.84%

Hence , 

Rate = 82.84 %