Multiple choice

A sum of Rs. 1230 is borrowed at 5% compound interest for 2 years on the condition that it is refunded in 2 equal installments - one at the end of the first year and the other at the end of the second. Find the amount of each installment.

  1. Rs. 637.50

  2. Rs. 661.50

  3. Rs. 655.50

  4. Rs. 650.61

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the installment. 1230 = x/(1.05) + x/(1.05)^2. 1230 = x(1/1.05 + 1/1.1025) = x(1.05 + 1)/1.1025 = x(2.05/1.1025). x = 1230 * 1.1025 / 2.05 = 661.50.

AI explanation

Let the equal installment be x, so its present value for the first year is x / 1.05 and for the second year is x / (1.05)^2. Set the sum of these present values equal to the borrowed amount, 1230 = x / 1.05 + x / 1.1025. Solving this equation by multiplying 1230 by 1.1025 and dividing by 2.1525 results in each installment being Rs. 661.50.

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