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% =
Compound interest =
Where
Compound interest of Rachel for 3 years =
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 =
Hence, the correct answer is INR 13,000.
