Multiple choice

The compound interest on a certain sum of money for 2 years, at 20% p.a, is Rs. 440. Find the simple interest for the same sum, at the same rate, for the same time.

  1. Rs. 400

  2. Rs. 500

  3. Rs. 250

  4. Rs. 350

  5. None of these

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A Correct answer
Explanation

Compound interest = P((1 + r/100)^n - 1) = 440. P((1 + 0.2)^2 - 1) = 440. P(1.44 - 1) = 440. P(0.44) = 440, so P = 1000. Simple interest = P * r * t / 100 = 1000 * 20 * 2 / 100 = 400.

AI explanation

For two years, the difference between compound interest and simple interest on a principal P at 20% is P times 20 divided by 100 squared, yielding 0.04P. Setting 0.04P equal to 440 gives a principal of 11000. The simple interest is 11000 times 20 times 2 divided by 100, resulting in Rs. 400.