Multiple choice

A certain sum is lent at compound interest for three years at rate of interests of 5%, 10% and 12% respectively for three consecutive years. Find the sum if the total interest for the 3 years is 5284.80.

  1. 18000

  2. 16000

  3. 15000

  4. 12000
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A Correct answer
Explanation

Let P be the sum. Amount after 3 years = P * 1.05 * 1.10 * 1.12 = P * 1.2936. Interest = 0.2936P = 5284.80. P = 5284.80 / 0.2936 = 18000.

AI explanation

Using the successive percentage change formula for compound interest, the total amount becomes the principal multiplied by 1.05, then 1.10, and then 1.12. The effective multiplication factor is 1.2936, meaning the total interest is 0.2936 times the principal. Setting 0.2936 multiplied by the principal equal to 5284.80 gives the principal as 18000.

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