Question

The simple interest on a certain sum of money at 9% is Rs.450 in 2 years. Find compound interest on the same at the same rate for 1 year, if interest is reckoned half yearly.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{P}\mathrm{be}\mathrm{the}\mathrm{principal}. \\ \mathrm{Rate},\mathrm{R}=9\%\mathrm{p}.\mathrm{a} \\ \mathrm{Time},\mathrm{T}=2\mathrm{yrs} \\ \mathrm{SI}=\mathrm{Rs}450 \\ \Rightarrow \frac{\mathrm{PRT}}{100}=450 \\ \Rightarrow \mathrm{P}\times 9\times 2=45000 \\ \Rightarrow \mathrm{P}=\frac{45000}{18}=2500 \\ \mathrm{So},\mathrm{required}\mathrm{sum}\mathrm{is}\mathrm{Rs}2500 \\ \mathrm{Now},\mathrm{P}=\mathrm{Rs}2500 \\ \mathrm{Rate}=\mathrm{R}=9\%\mathrm{p}.\mathrm{a}=\left(\frac{9}{2}\right)\%\mathrm{per}\mathrm{half}\mathrm{year} \\ \mathrm{time},\mathrm{n}=1\mathrm{yr}=2\mathrm{half}\mathrm{yrs} \\ \mathrm{Amount},\mathrm{A}=\mathrm{P}{\left[1+\frac{\mathrm{R}}{100}\right]}^{\mathrm{n}}=2500{\left[1+\frac{9}{200}\right]}^2=2500\times \frac{209}{200}\times \frac{209}{200}=2730.0625 \\ \mathrm{CI}=\mathrm{A}-\mathrm{P}=2730.0625-2500=\mathrm{Rs}230.0625 \end{gathered}$$