Multiple choice

A man borrows Rs. 15,150, which is to be paid back with compound interest at a rate of 2% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be?

  1. Rs. 7,803

  2. Rs. 7,808

  3. Rs. 2,601

  4. Rs. 5,050

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

For two equal annual installments P at rate r=2%, the formula is Total = P/(1+r) + P/(1+r)^2. 15150 = P/1.02 + P/(1.02)^2. 15150 = P * (1/1.02 + 1/1.0404) = P * (1.02 + 1)/1.0404 = P * 2.02/1.0404. P = 15150 * 1.0404 / 2.02 = 7803.

AI explanation

When a loan is repaid in equal yearly instalments, the principal is the present value of all instalments, so we use the formula P = (x / (1 + r)) + (x / (1 + r) squared). Substituting the given values gives 15150 = (x / 1.02) + (x / 1.0404). Finding a common denominator gives 15150 = (1.0404x + 1.02x) / 1.0608, which simplifies to 15150 x 1.0608 = 2.0604x. Solving for x gives 16070.52 / 2.0604, which results in an instalment of Rs. 7,803.

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