Question

The simple interest on a sum of money for 2 years at 4% per annum is Rs 450. Find the compund interest on this sum at the same rate for 1 year if interest is reckoned semi annually?

Answer 1

$$\begin{gathered} \mathbf{CALCULATION}\mathbf{}\mathbf{OF}\mathbf{}\mathbf{SUM}\mathbf{}\mathbf{FROM}\mathbf{}\mathbf{SI}\mathbf{}\mathbf{:} \\ \mathrm{Let}\mathrm{the}\mathrm{principal},\mathrm{P}=\mathrm{Rs}\mathrm{x} \\ \mathrm{Time},\mathrm{T}=2\mathrm{yrs} \\ \mathrm{Rate}=4\%\mathrm{p}.\mathrm{a} \\ \mathrm{SI}=\mathrm{Rs}450 \\ \Rightarrow \frac{\mathrm{PRT}}{100}=450 \\ \Rightarrow \frac{\mathrm{x}\times 4\times 2}{100}=450 \\ \Rightarrow \mathrm{x}=5625 \\ \mathrm{So},\mathrm{P}=\mathrm{Rs}5625 \\ \mathbf{CALCULATION}\mathbf{}\mathbf{OF}\mathbf{}\mathbf{CI}\mathbf{}\mathbf{:} \\ \mathrm{Principal},\mathrm{P}=\mathrm{Rs}5625 \\ \mathrm{Rate},\mathrm{R}=4\%\mathrm{p}.\mathrm{a}=2\%\mathrm{per}\mathrm{half}\mathrm{year} \\ \mathrm{Time},\mathrm{n}=1\mathrm{y}=2\mathrm{half}\mathrm{yrs} \\ \mathrm{Amount},\mathrm{A}=\mathrm{P}{\left[1+\frac{\mathrm{R}}{100}\right]}^{\mathrm{n}} \\ =5625{\left[1+\frac{2}{100}\right]}^2 \\ =5625\times \frac{51}{50}\times \frac{51}{50} \\ =5852.25 \\ \mathrm{Now},\mathrm{CI}=\mathrm{A}-\mathrm{P}=5852.25-5625=\mathrm{Rs}227.25 \end{gathered}$$