Multiple choice

A: Calculate the difference between the simple interest and the compound interest on Rs. $4,000$ in $2$ years at $8 \%$ per annum compounded yearly. B: On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simpled interest for a year is Rs. $180$/-. Find the sum lent out, if the rate of interest in both the cases is $10 \%$ per annum. Then, find $10A + B$.

  1. $72256$
  2. $720256$
  3. $722056$
  4. $722506$
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A Correct answer
Explanation

Part A: Difference between CI and SI for 2 years = P * (r/100)^2 = 4000 * (0.08)^2 = 4000 * 0.0064 = 25.6. Part B: Difference between CI (half-yearly) and SI for 1 year = P * ((1 + r/200)^2 - 1) - P * (r/100) = 180. With r=10, P * ((1.05)^2 - 1 - 0.1) = 180 => P * (1.1025 - 1.1) = 180 => P * 0.0025 = 180 => P = 72000. Then 10A + B = 10(25.6) + 72000 = 256 + 72000 = 72256.

AI explanation

For part A, the difference between simple and compound interest for two years is P(r/100)^2 = 4000(8/100)^2 = 25.6, so 10A = 256. For part B, the difference between half-yearly compound interest and simple interest for one year is P(r/200)^2 = P(10/200)^2 = P/400. Since the difference is Rs. 180, the principal B = 180 * 400 = 72000. The final expression is 10A + B = 256 + 72000 = 72256. The result is 72256.

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