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 ₹897, what was the sum that Rachel had invested?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. ₹13,000.
Let The investment of Peter in a scheme be 2x
& investment of Rachel in a scheme be x
Peter invested money at the rate of simple interest 10% for 2 years
Rachel invested money at rate of compound interest 10% for 3 years
Formula used
S.I. = PRT/100
where, P = principal, R = rate , T = time
C.I. = Principal (1 + Rate/100)time - Principal
Calculation
⇒ S.I. = 2x × 10 × 2/100 = 4x/10
⇒ C.I. = x(1 + 10/100)3 - x = (1331x - 1000x)/1000 = 331x/1000
GIven
⇒ S.I. - C.I. = ₹897
⇒ 4x/10 - 331x/1000 = 897
⇒ 400x - 331x = 897000
⇒ 69x = 897000
⇒ x = ₹13000
Hence, Rachel's investment = ₹13000