Mathematics for FinanceMTP June 24 Series IQuestion 1185 of 512
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If the difference between the compound interest compounded annually and simple interest on a certain amount at 10%\displaystyle 10\% per annum for two years is 372\displaystyle 372, then the principal amount is.

Options

A37,000\displaystyle 37,000
B37,200\displaystyle 37,200
C37,500\displaystyle 37,500
DNone of these
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Correct Answer

✅ Option b — 37,200\displaystyle 37,200

All Options:

  • A37,000\displaystyle 37,000
  • B37,200\displaystyle 37,200
  • C37,500\displaystyle 37,500
  • DNone of these

Detailed Solution & Explanation

Let the principal be P\displaystyle P. The rate of interest is r=10%\displaystyle r = 10\% p.a., so i=10100=0.10\displaystyle i = \frac{10}{100} = 0.10. The time period is t=2\displaystyle t = 2 years. The formula for the difference between Compound Interest (CI\displaystyle CI) and Simple Interest (SI\displaystyle SI) for a 2\displaystyle 2-year period is: CI−SI=P×i2CI - SI = P \times i^2 Given that the difference is Rs. 372\displaystyle \text{Rs. }372: 372=P×(0.10)2372 = P \times (0.10)^2 372=P×0.01372 = P \times 0.01 Solving for P\displaystyle P: P=3720.01=37,200P = \frac{372}{0.01} = 37,200 Thus, the principal amount is Rs. 37,200\displaystyle \text{Rs. }37,200. Hence, **Option B** is the correct answer.

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