Question

What sum of money will amount to Rs 21296 in 3 years at 10% per annum, compounded annually?

Answer 1

$$\begin{gathered} \mathrm{Let}Pbe\mathrm{the}\mathrm{sum}. \\ \mathrm{Rate}\mathrm{of}\mathrm{interest},\mathit{}R=10\% \\ \mathrm{Time},n\mathit{}=3\mathrm{years} \\ \mathrm{Now},A=P\times {\left(1+\frac{10}{100}\right)}^3 \\ =\mathrm{Rs}.\mathit{}P\times {\left(\frac{100+10}{100}\right)}^3 \\ =\mathrm{Rs}.P\times {\left(\frac{110}{100}\right)}^3 \\ =\mathrm{Rs}.P\mathit{\times }\left(\frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}\right) \\ =\mathrm{Rs}.\frac{1331P}{1000} \\ \mathrm{However},\mathrm{amount}=\mathrm{Rs}.21296 \\ \mathrm{Now},\mathrm{Rs}.21296=\mathrm{Rs}.\frac{1331P}{1000} \\ \Rightarrow \mathrm{Rs}.\left(\frac{21296\times 1000}{1331}\right)=P \\ \therefore \mathit{}P=\mathrm{Rs}.16000 \\ \mathrm{Hence},\mathrm{the}required\mathrm{sum}\mathrm{is}\mathrm{Rs}.16000. \end{gathered}$$