Question

I borrowed a certain sum at compound interest at the rate of 15%per annum. at the end of 2 years I paid rs5290as amounthow much sum had I borrowed

Answer 1

Hi,

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{sum}\mathrm{borrowed}=\mathrm{Rs}\mathrm{P} \\ \mathrm{rate},\mathrm{r}=15\%\mathrm{p}.\mathrm{a}. \\ \mathrm{Time},\mathrm{n}=2\mathrm{yrs} \\ \mathrm{Amount},\mathrm{A}=\mathrm{Rs}5290 \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{r}}{100}\right)}^{\mathrm{n}} \\ \Rightarrow 5290=\mathrm{P}{\left[1+\frac{15}{100}\right]}^2 \\ \Rightarrow 5290=\mathrm{P}{\left(1+\frac{3}{20}\right)}^2 \\ \Rightarrow 5290=\mathrm{P}\times \frac{23}{20}\times \frac{23}{20} \\ \Rightarrow \mathrm{P}=10\times 20\times 20=4000 \\ \mathrm{So},\mathrm{sum}\mathrm{borrowed}=\mathrm{Rs}4000 \end{gathered}$$

Regards