Question

The difference between the compound interest and the simple interest on a certain sum of money at 5% per annum for 2 years is rs. 1.50. find the sum.

Answer 1

Answer:

Concept:

Compound interest and simple interest

Step-by-step explanation:

          $\begin{gathered}\text { Let the Sum be } P^{\prime} \quad P=\text { ? } \\(C I-S I) \text { for } 2 \text { year }=R 1.50 \\P\left(1+\frac{R}{100}\right)^t-P-\frac{P R \times t}{100}=\frac{150}{100} \\P\left(\frac{100+R}{100}\right)^{2}-P-\frac{2 P R}{100}=\frac {3}{2}\end{gathered}$

          $\begin{aligned}(a+b)^{2} &=a^{2}+b^{2}+2 a b \\ P & \frac{\left(100^{2}+R^{2}+200 R\right)}{100^{2}}-\left[P+\frac{2 P R}{100}\right]=\frac{3}{2} \end{aligned}$

          $\begin{aligned}&\frac{100^{2} P+P R^{2}+200 P R}{100^{2}}-\left[\frac{100 P+2 P R}{100}\right] \times \frac{100}{100}=\frac{3}{2} \\&\frac{100^{2} P+P R^{2}+200 P R-100^{2} P-200 P R}{100^{2}}=\frac{3}{2}\end{aligned}$

                          $\frac{P R^{2}}{100^{2}}=\frac{3}{2}$

                       $\frac{P \times S^{2}}{10,000}=\frac{3}{2}$

                        $\frac{P \times 25}{10000}=\frac{3}{2}$

                          P = $\frac{3}{2}$ × 400

                            P = 600

Hence The difference between the compound interest and the simple interest on a certain sum of money at 5% per annum for 2 years is Rs. 1.50. The sum is Rs.600

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