Multiple choice

Ajay takes a loan of Rs. 19,860 to buy a bike, to be repaid in 3 equal annual installments. The bank charges an interest rate of 10% per annum on the outstanding balance. How much should Ajay pay each year?

  1. Rs. 7,150

  2. Rs. 7,190

  3. Rs. 7,986

  4. Rs. 7,290

  5. Rs. 7,340
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is an annuity problem. P = 19860, r = 0.1, n = 3. Formula: P = X * [1 - (1+r)^-n] / r. 19860 = X * [1 - (1.1)^-3] / 0.1. 19860 = X * [1 - 0.7513] / 0.1. 19860 = X * 2.4868. X = 19860 / 2.4868 = 7986.

AI explanation

The present value of the three equal installments must equal the initial loan amount. If each installment is x, then 19860 equals x divided by 1.10, plus x divided by 1.10 squared, plus x divided by 1.10 cubed. This simplifies to 19860 equals x multiplied by 2.4868. Dividing 19860 by 2.4868 gives an annual installment of Rs. 7,986.

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