Question

In how much time will a sum of Rs 1600 amount to Rs 1852.20 at 5% per annum compound interest?

Answer 1

$$\begin{gathered} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ 1852.20=1600{\left(1+\frac{5}{100}\right)}^{\mathrm{n}} \\ \frac{1852.20}{1600}={\left(1.05\right)}^{\mathrm{n}} \\ {\left(1.05\right)}^{\mathrm{n}}=1.157625 \\ {\left(1.05\right)}^{\mathrm{n}}={\left(1.05\right)}^3 \\ \mathrm{On}\mathrm{comparing}\mathrm{both}\mathrm{the}\mathrm{sides},\mathrm{we}\mathrm{get}: \\ \mathrm{n}=3 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{time}\mathrm{is}\mathrm{three}\mathrm{years}. \end{gathered}$$