Multiple choice

A sum of Rs. $11000$ was taken as a loan. This is to be repaid in two equal instalments. If the rate of interest be $20\%$ compounded annually, then the value of each instalment is

  1. Rs. $8420$
  2. Rs. $7920$
  3. Rs. $7200$
  4. Rs. $7000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the instalment be X. 11000 = X / (1.2) + X / (1.2)^2. 11000 = X * (1/1.2 + 1/1.44) = X * (1.2 + 1) / 1.44 = X * 2.2 / 1.44. X = 11000 * 1.44 / 2.2 = 5000 * 1.44 = 7200.

AI explanation

Using the formula for the present value of equal installments P = x/(1 + r/100) + x/(1 + r/100)^2, we have 11000 = x/(1 + 20/100) + x/(1 + 20/100)^2. This simplifies to 11000 = x/(6/5) + x/(36/25), which equals 5x/6 + 25x/36. Finding a common denominator gives 11000 = 30x/36 + 25x/36 = 55x/36, so x = 11000 * 36 / 55, making each installment 7200.

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