# | | 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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