Multiple choice

The compound interest on Rs. $8000$ for $1$ year at $5$ % p.a. payable half-yearly is:

  1. Rs. $800$
  2. Rs. $810$
  3. Rs. $400$
  4. Rs. $405$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Principal = 8000, Rate = 5% p.a. compounded half-yearly (2.5% per 6 months). Time = 1 year (2 periods). Amount = 8000 * (1.025)^2 = 8000 * 1.050625 = 8405. Interest = 8405 - 8000 = 405.

AI explanation

For interest payable half-yearly, the formula for compound interest becomes CI = P * [(1 + R/(2*100))^(2n) - 1]. Substituting the given values, we get CI = 8000 * [(1 + 5/200)^2 - 1], which simplifies to 8000 * [(41/40)^2 - 1]. This evaluates to 8000 * (1681/1600 - 1), resulting in an interest of Rs. 405.

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