question_answer 19)

                Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?

Answer:

                For Fabina SI on Rs 12, 500 at 12% p.a. for 3 years \[=\frac{12,500\times 12\times 3}{100}=\text{Rs}\,4,500\] For Radha P = Res 12, 500 R = 10% of per annum \[n=3\] years \[\therefore \]  \[A=P\,{{\left( 1+\frac{R}{100} \right)}^{n}}\] \[=12,500{{\left( 1+\frac{10}{100} \right)}^{3}}\] \[=12,500{{\left( 1+\frac{1}{10} \right)}^{3}}\] \[=12,500\,{{\left( \frac{11}{10} \right)}^{3}}\] \[=12,500\,\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}\] = Rs 16, 637.50 \[\therefore \]  CI = A ? P                 = Rs 16, 637.50 ? Rs 12, 500 = Rs 4,137.50 Difference between CI and SI = Rs 4,500 - Rs 4,137.50 = Rs 362.50 Hence, Fabina pays more by Rs 362.50.