Multiple choice

On what sum will the compound interest at $5\%$ p.a. for $2$ years compounded annually be Rs. $1,640$?

  1. $16,000$
  2. $630.50$
  3. $425.76$
  4. $1,640$
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A Correct answer
Explanation

Compound interest formula: CI = P * ((1 + r/100)^n - 1). 1640 = P * ((1 + 0.05)^2 - 1) = P * (1.1025 - 1) = P * 0.1025. P = 1640 / 0.1025 = 16000.

AI explanation

Using the compound interest formula CI = P[(1 + R/100)^n - 1], we substitute the given values to get 1640 = P[(1 + 5/100)^2 - 1]. This simplifies to 1640 = P[(21/20)^2 - 1], which becomes 1640 = P(41/400). Solving for the principal gives P = (1640 * 400) / 41 = 16000. The required sum is Rs. 16,000.

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