Multiple choice

The difference between the compound interest compounded half yearly for 1 year and the simple interest for 1 year on a certain sum of money lent out at 8% per annum is Rs. 64. What is the sum (in Rs)?

  1. 40,000

  2. 42,000

  3. 44,000

  4. 44,800

  5. None of these
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A Correct answer
Explanation

CI for 1 year compounded half-yearly at 8% = P * (1 + 0.04)^2 - P = P * (1.0816 - 1) = 0.0816P. SI for 1 year at 8% = 0.08P. Difference = 0.0016P = 64. P = 64 / 0.0016 = 40000.

AI explanation

Using the half-yearly compound interest formula, the effective annual rate for 8% compounded semi-annually is calculated as (1 + 0.08/2)^2 - 1 = 0.0816, or 8.16%. The difference between this compound interest rate and the 8% simple interest rate is 0.16%. Given that this 0.16% difference equals Rs. 64, the principal sum is calculated as 64 / 0.0016 = 40,000.

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