| | Question 31

A money lender borrows money at 5% per annum and pays the interest at the end of the year. He lends it at 8% per annum compound interest compounded half-yearly and receives the interest at the end of the year. In this way, he gains Rs 120.08 a year. The amount of money he borrows.
(A) Rs 3200
(B) Rs 3400
(C) Rs 3800
(D) Rs 4200


Answer: (C)

Explanation: Case (1)Rate = 5 %
time = 1 year
Case (2) When interest is compounded half yearly
Rate = 8/2 =4%
Time = 1 x 2 = 2 years
Effective rate % for 2 years = 4 + 4 + 4×4/100 = 8.16 %
Difference in rates= 8.16% – 5 = 3.16 %
Given that he gains 120.08. So,
3.16 -> 120.08
1 -> 38
100 -> 3800
Hence, the amount of money he borrows Rs 3800

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