Mathematics for FinancePYQ June 24Question 1259 of 512
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The difference between the compound interest amount and the simple interest amount for a period of two years, at same interest rate r\displaystyle r is

Options

AP×r\displaystyle P \times r
BP×r2\displaystyle P \times r^2
CP×2×r\displaystyle P \times 2 \times r
DP2×r\displaystyle P^2 \times r
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Correct Answer

✅ Option b — P×r2\displaystyle P \times r^2

All Options:

  • AP×r\displaystyle P \times r
  • BP×r2\displaystyle P \times r^2
  • CP×2×r\displaystyle P \times 2 \times r
  • DP2×r\displaystyle P^2 \times r

Detailed Solution & Explanation

**Derivation of Difference between Compound and Simple Interest** Given: - Principal = P\displaystyle P - Interest rate = r\displaystyle r (in decimals) - Time (t\displaystyle t) = 2\displaystyle 2 years **Step 1: Write down Simple Interest (SI\displaystyle SI) and Compound Interest (CI\displaystyle CI)** - SI=P×r×2=2PrSI = P \times r \times 2 = 2Pr - CI=P(1+r)2−P=P(1+2r+r2)−P=2Pr+Pr2CI = P(1 + r)^2 - P = P(1 + 2r + r^2) - P = 2Pr + Pr^2 **Step 2: Calculate the difference** Difference=CI−SI=(2Pr+Pr2)−2Pr=Pr2\text{Difference} = CI - SI = (2Pr + Pr^2) - 2Pr = Pr^2 Thus, the difference is P×r2\displaystyle P \times r^2. Hence, **Option B** is the correct answer.

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