Multiple choice

An amount of Rs 12820 due 3 years hence, is fully repaid in three annual instalments starting after 1 year. The first instalment is 1/2 the second instalment and the second instalment is 2/3 of the third instalment. If the rate of interest is 10% per annum, find the first instalment.

  1. Rs 2400

  2. Rs 1800

  3. Rs 2000

  4. Rs 2500
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C Correct answer
Explanation

Let the instalments be x, 2x, and 3x. The present value of these instalments at 10% interest is x/1.1 + 2x/(1.1^2) + 3x/(1.1^3) = 12820. Solving this equation yields x = 2000.

AI explanation

Let the first instalment be x, making the second instalment 2x and the third instalment 3x. Using the present value formula for each instalment at 10 percent interest, the equation becomes 12820 equals x divided by 1.1 plus 2x divided by 1.21 plus 3x divided by 1.331. Converting these fractions gives 12820 equals 11x divided by 12.1 plus 2420x divided by 1464.1 plus 3000x divided by 1464.1, which simplifies to 12820 equals 66.55x, yielding a first instalment of 2000.

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