Multiple choice

A loan was repaid in two annual installments of Rs. 1210 each. If the rate of interest be 10% per annum compounded annually, then the sum borrowed was

  1. Rs. 2000

  2. Rs. 2500

  3. Rs. 2100

  4. Rs. 3000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the sum. The present value of two installments of 1210 at 10% interest is: 1210 / 1.1 + 1210 / (1.1)^2 = 1100 + 1000 = 2100.

AI explanation

To find the present value of the loan, we calculate the principal for each installment using the present value formula for compound interest: Present Value equals Installment divided by (1 plus Rate divided by 100) raised to the power of the number of years. The first installment of Rs. 1210 due after one year has a present value of 1210 divided by 1.10, which is Rs. 1100. The second installment due after two years has a present value of 1210 divided by 1.21, which is Rs. 1000. The total sum borrowed is the sum of these present values: 1100 plus 1000 equals Rs. 2100.

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