Question

In how much time would Rs 5000 amount to Rs 6655 at 10% per annum compound interest?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{time}\mathrm{period}\mathrm{be}\mathrm{n}\mathrm{years}. \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \mathrm{CI}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}}-\mathrm{P} \\ 6,655=5,000{\left(1+\frac{10}{100}\right)}^{\mathrm{n}}-5,000 \\ 11,655=5,000{\left(1.10\right)}^{\mathrm{n}} \\ {\left(1.1\right)}^{\mathrm{n}}=\frac{11,655}{5,000} \\ {\left(1.1\right)}^{\mathrm{n}}=2.331 \\ {\left(1.1\right)}^{\mathrm{n}}={\left(1.1\right)}^3 \\ \mathrm{On}\mathrm{comparing}\mathrm{both}\mathrm{the}\mathrm{sides},\mathrm{we}\mathrm{get}: \\ \mathrm{n}=3 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{time}\mathrm{is}\mathrm{three}\mathrm{years}. \end{gathered}$$