Question

10. rishi borrowed rs 20000 for 3 years at the rate of 8.5% p.a. simple interest, while john borrowed the same amount for the same period at 8% p.a. compounded annually who paid less interest and by how much?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Rishi}\mathrm{borrowed}\mathrm{Rs}20000\mathrm{for}3\mathrm{years}\mathrm{at}\mathrm{the}\mathrm{rate}\mathrm{of}8.5\%\mathrm{p}.\mathrm{a} \\ \mathrm{So},\mathrm{Interest}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{T}}{100} \\ =\frac{20000\times 8.5\times 3}{100} \\ =5100 \\ \mathrm{So},\mathrm{interest}\mathrm{paid}\mathrm{by}\mathrm{Rishi}\mathrm{is}\mathrm{Rs}5100. \\ \mathrm{John}\mathrm{borrowed}\mathrm{Rs}20000\mathrm{for}3\mathrm{years}\mathrm{at}8\%\mathrm{p}.\mathrm{a}\mathrm{compounded}\mathrm{annually}. \\ \mathrm{So},\mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ =20000{\left(1+\frac{8}{100}\right)}^3 \\ =20000{\left(\frac{108}{100}\right)}^3 \\ =20000\times \frac{1259712}{1000000} \\ =25194.25 \\ \mathrm{So},\mathrm{interest}\mathrm{piad}\mathrm{by}\mathrm{John}=\mathrm{Rs}\left(25194.25-20000\right)=\mathrm{Rs}5194.25 \\ \mathrm{So},\mathrm{Rishi}\mathrm{paid}\mathrm{less}\mathrm{interest}. \end{gathered}$$
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