Multiple choice

A money-lender borrows money at 4% per annum and pays the compound interest at the end of the year. He lends it at 6% p.a. compounded half-yearly and receives the interest at the end of the year. In this way, he gains Rs. 104.50 in that year. How much money does he borrow?

  1. Rs. 4850

  2. Rs. 4500

  3. Rs. 5000

  4. Rs. 5200

  5. Rs. 6000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The money-lender borrows at 4% compounded annually, so the cost is 0.04P. He lends at 6% compounded half-yearly, which is equivalent to an annual rate of (1 + 0.06/2)^2 - 1 = 1.03^2 - 1 = 0.0609, or 6.09%. The gain is 0.0609P - 0.04P = 0.0209P = 104.50. Solving for P gives 104.50 / 0.0209 = 5000.

AI explanation

Let the borrowed sum be P, so the money-lender pays 4% compound interest annually, making his cost 0.04P. He lends the money at 6% compounded half-yearly, meaning the rate is 3% per half year, so his interest received is P multiplied by the quantity 1.03 squared minus 1, which equals 0.0609P. His gain is the difference between the interest received and the interest paid, so 0.0609P minus 0.04P equals 0.0209P, and equating this to Rs. 104.50 gives P equal to Rs. 5000.

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