Question

Simple interest on a sum of money for 5 years at 8% per Anjum is ₹22,000. What will be the compound interest on that sum at the same rate for 3 years

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{sum},\mathrm{P}=\mathrm{Rs}\mathrm{x} \\ \mathrm{Rate},\mathrm{R}=8\%\mathrm{p}.\mathrm{a}. \\ \mathrm{Time},\mathrm{T}=5\mathrm{yrs} \\ \mathrm{SI}=\mathrm{Rs}22000 \\ \Rightarrow \frac{\mathrm{PRT}}{100}=22000 \\ \Rightarrow \frac{\mathrm{x}\times 8\times 5}{100}=22000 \\ \Rightarrow \mathrm{x}=55000 \\ \mathrm{So},\mathrm{P}=\mathrm{Rs}55000 \\ \mathrm{Now},\mathrm{P}=\mathrm{Rs}55000;\mathrm{Rate},\mathrm{R}=8\%\mathrm{p}.\mathrm{a}.;\mathrm{Time},\mathrm{n}=3\mathrm{yrs} \\ \mathrm{Amount},\mathrm{A}=\mathrm{P}{\left[1+\frac{\mathrm{R}}{100}\right]}^{\mathrm{n}}=55000{\left[1+\frac{8}{100}\right]}^3 \\ =55000\times {\left(\frac{108}{100}\right)}^3 \\ =\mathrm{Rs}69284.160 \\ \mathrm{CI}=\mathrm{A}-\mathrm{P}=69284.160-550000=\mathrm{Rs}14284.160 \end{gathered}$$