Question

Amit borrowed Rs 16000 at $17\frac{1}{2}\%$ per annum simple interest. On the same day, he lent it to Ashu at the same rate but compounded annually. What does he gain at the end of 2 years?

Answer 1

$$\begin{gathered} \mathrm{Amount}\mathrm{to}\mathrm{be}\mathrm{paid}\mathrm{by}\mathrm{Amit}: \\ \mathrm{SI}=\frac{\mathrm{PRT}}{100} \\ =\frac{16000\times 17.5\times 2}{100} \\ =\mathrm{Rs}5,600 \\ \mathrm{Amount}\mathrm{gained}\mathrm{by}\mathrm{Amit}: \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ =\mathrm{Rs}16,000{\left(1+\frac{17.5}{100}\right)}^2 \\ =\mathrm{Rs}16,000{\left(1.175\right)}^2 \\ =\mathrm{Rs}22,090 \\ \mathrm{We}\mathrm{know}\mathrm{that}: \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs}22,090-\mathrm{Rs}16,000 \\ =\mathrm{Rs}6090 \\ \mathrm{Amit}\text{'}\mathrm{s}\mathrm{gain}\mathrm{in}\mathrm{the}\mathrm{whole}\mathrm{transaction}=\mathrm{Rs}6,090-\mathrm{Rs}5,600 \\ =\mathrm{Rs}490 \end{gathered}$$