question_answer 20)

                I borrowed Rs 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what excess amount would I have to pay?

Answer:

                At simple interest SI on Rs 12,000 at 6% per annum for 2 years \[=\frac{12,000\times 6\times 2}{100}=\text{Rs}1,440\] At compound interest P = Rs 12,000 R = 6% per annum \[n=2\] years \[\therefore \]  \[A=P\,{{\left( 1+\frac{R}{100} \right)}^{n}}\] \[=12,000{{\left( 1+\frac{6}{100} \right)}^{2}}\] \[=12,000\,{{\left( 1+\frac{3}{50} \right)}^{2}}\] \[=12,000{{\left( \frac{53}{50} \right)}^{2}}\] \[=12,000\times \frac{53}{50}\,\times \frac{53}{50}\] = Rs 13,483.20 \[\therefore \]  CI = A ? P = Rs 13,483.20 ? Rs 12,000 = Rs 1,483.20 \[\therefore \] Excess amount = Rs 1,483.20 ? Rs 1,440 = Rs 43.20 Hence, I would have to pay to him an excess amount of Rs 43.20.