What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?

Solution (By Examveda Team)

$$\eqalign{ & 1{\text{ year CI}} = 1{\text{ year SI}} \cr & {\text{SI}} = \frac{{P \times R \times T}}{{100}} \cr & = \frac{{50000 \times 8 \times 1}}{{100}} \cr & = 4000 \cr & {\text{Compound interest at half yearly}} \cr & {\text{Rate}} = \frac{8}{2} = 4\% \cr & {\text{Time}} = 1 \times 2 = 2{\text{ years}} \cr & A = P{\left( {1 + \frac{R}{{100}}} \right)^n} \cr & A = 50000{\left( {1 + \frac{4}{{100}}} \right)^2} \cr & A = 50000 \times \frac{{104}}{{100}} \times \frac{{104}}{{100}} \cr & A = 5 \times 10816 \cr & A = 54080 \cr & {\text{CI}} = 54080 - 50000 = 4080 \cr & {\text{Difference between the interest of on year}} \cr & = 4080 - 4000 \cr & = 80 \cr} $$