Given,
Principal = Rs.10000
Rate = 20%
Time = 2 year
Hence,
Compound interest\(={P}[({1}+\frac{R}{100})^T-{1}]\)
\(={10000}[({1}+\frac{20}{100})^2-{1}]\)
\(={10000}[(\frac{6}{5})^2-{1}]\)
\(={10000}\times(\frac{11}{25})\) = Rs. 4400
If interest compounded half yearly,
Rate \(=\frac{20}{2} ={10}\text%\)
Time \(={2\times2}\) = 4 half years
Hence,
Compound interest \(={P}[({1}+\frac{R}{100})^T-{1}]\)
\(={10000}[({1}+(\frac{10}{100})^4-{1}]\)
\(={10000}[(\frac{11}{10})^4-{1}]\)
\(={10000}\times\frac{4641}{10000}\) = Rs. 4641
So,
If Rakesh can earn = Rs.(4641 – 4400 ) = Rs.241 more
