Question : Peter invested a certain sum of money in a scheme paying 10% simple interest per annum, while Rachel invested half of the sum that Peter invested in a scheme paying 10% interest per annum compounded annually. Also, while Peter invested for 2 years, Rachel invested for 3 years. If the difference in the interest earned by Peter and Rachel was INR 897, what was the sum that Rachel had invested?
Option 1: INR 13,000
Option 2: INR 12,900
Option 3: INR 13,100
Option 4: INR 12,960
Correct Answer: INR 13,000
Solution : Let investment of Peter = INR 100 at 10% simple interest (SI) So investment of Rachel = INR 50 at 10% compound interest (CI) The simple interest of Peter for 2 years at 10% = $\frac{10×2}{100}\times 100$ = INR 20 Compound interest = $\text{P}(1+\frac{\text{R}}{100})^t - \text{P}$ Where $P$ is the principal, $R$ is the rate of interest per annum and $t$ is time. Compound interest of Rachel for 3 years = $50(1+\frac{10}{100})^3 -50$ = INR 16.55 So, difference = 20 – 16.55 = 3.45 The difference in the interest earned by Peter and Rachel was = INR 897 So, the investment of Rachel = $\frac{897}{3.45}\times 50$ = INR 13,000 Hence, the correct answer is INR 13,000.
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