Multiple choice

A sum is invested for three years at compound interest. The rates of compound interest for the first, second and third years are $8 \% $, $10 \%$ and $20 \%$ respectively. If the sum amounts to Rs$14,256$ at the end of three years, find the sum.

  1. Rs$10,000$
  2. $9,000$
  3. $8,000$
  4. $12,000$
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A Correct answer
Explanation

Let the sum be P. The amount after 3 years is P * (1 + 8/100) * (1 + 10/100) * (1 + 20/100) = 14256. This is P * (1.08) * (1.1) * (1.2) = 14256. P * 1.4256 = 14256, so P = 10000.

AI explanation

Using the successive percentage change formula for compound interest, the relationship between the sum P and the final amount is 14256 = P * (1 + 8/100) * (1 + 10/100) * (1 + 20/100). This simplifies to 14256 = P * (108/100) * (110/100) * (120/100), which further reduces to 14256 = P * 1.4256. Dividing both sides by 1.4256 gives the original sum of Rs. 10000.

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