Multiple choice

Rajesh took a loan of Rs. 67,100 from his employer at 20% per annum under compound interest, compounded annually, and agreed to repay it in four equal annual instalments, an instalment being paid at the end of each year. Find the value (in Rs.) of each instalment.

  1. 25,920

  2. 13,420

  3. 10,416

  4. None of these
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A Correct answer
Explanation

Using the formula for equal annual installments for compound interest: P = X * [1 - (1+r)^-n] / r, where X is the installment. 67100 = X * [1 - (1.2)^-4] / 0.2. 67100 = X * [1 - 0.48225] / 0.2 = X * 2.58875. X = 67100 / 2.58875 = 25920.

AI explanation

The present value formula for installments under compound interest is P = X/(1 + r/100)^1 + X/(1 + r/100)^2 + ... + X/(1 + r/100)^n, where P is the principal and X is the installment. Substituting the given values gives 67100 = X/1.2 + X/1.44 + X/1.728 + X/2.0736. Finding a common denominator gives 67100 = (1.728X + 1.44X + 1.2X + X)/2.0736, which simplifies to 67100 = 5.368X/2.0736. Solving for X gives 67100 times 2.0736 divided by 5.368 equals 25920, so each installment is Rs. 25920.

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