Multiple choice

If the compound interest on a certain sum for 2 years at 20% p.a. is Rs. 44, what would be the simple interest?

  1. Rs. 40

  2. Rs. 42

  3. Rs. 43

  4. Rs. 44
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A Correct answer
Explanation

CI = P((1+r/100)^n - 1). 44 = P((1.2)^2 - 1) = P(1.44 - 1) = 0.44P. So P = 100. SI = (P*r*t)/100 = (100*20*2)/100 = 40.

AI explanation

Using the identity for the difference between compound interest and simple interest over two years, the difference equals P times R squared divided by 100 squared. Substituting the given values, 44 minus SI equals P times 400 divided by 10000, which simplifies to 0.04 times P. Because the compound interest formula for two years at 20% gives 44 equals P times 0.44, the principal P is exactly 100. Plugging P equal to 100 back into the difference equation gives 44 minus SI equals 4, meaning the simple interest is Rs. 40.

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