Question

At what rate percent per annum will Rs 1620 amount to Rs 1962 in 3 years 2 months?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{R}\%\mathrm{p}.\mathrm{a}.\mathrm{be}\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{interest}. \\ \mathrm{Now},\mathrm{Principal},\mathrm{P}=\mathrm{Rs}1620 \\ \mathrm{Amount},\mathrm{A}=\mathrm{Rs}1962 \\ \mathrm{Time},\mathrm{T}=3\mathrm{yr}2\mathrm{months}=3\frac{2}{12}\mathrm{yrs}=3\frac{1}{6}\mathrm{yrs}=\frac{19}{6}\mathrm{yrs} \\ \mathrm{Now},\mathrm{SI}=\frac{\mathrm{PRT}}{100} \\ \Rightarrow \mathrm{A}-\mathrm{P}=\frac{\mathrm{PRT}}{100} \\ \Rightarrow 1962-1620=\frac{1620\times \mathrm{R}\times 19}{6\times 100} \\ \Rightarrow 342=\frac{1620\times \mathrm{R}\times 19}{6\times 100} \\ \Rightarrow 18=\frac{1620\times \mathrm{R}}{6\times 100} \\ \Rightarrow \mathrm{R}=\frac{18\times 600}{1620} \\ \Rightarrow \mathrm{R}=6.67 \\ \mathrm{So},\mathrm{rate}\mathrm{is}6.67\%\mathrm{p}.\mathrm{a}. \end{gathered}$$