Mathematics for FinancePYQ Sep 24Question 1268 of 512
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At a certain rate of interest per annum, the difference between the compound interest and simple interest on 3,00,000\displaystyle 3,00,000 for two years is 2,400\displaystyle 2,400, then the rate of interest per annum is:

Options

A4%\displaystyle 4\%
B2%\displaystyle 2\%
C6%\displaystyle 6\%
D8%\displaystyle 8\%
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Correct Answer

✅ Option d — 8%\displaystyle 8\%

All Options:

  • A4%\displaystyle 4\%
  • B2%\displaystyle 2\%
  • C6%\displaystyle 6\%
  • D8%\displaystyle 8\%

Detailed Solution & Explanation

**Derivation of Rate of Interest** *Note: The question contains a typo in the Principal amount, stating it is 3,00,000. In standard CA Foundation problems, this Principal is 3,75,000, which yields a whole-number solution of 8%. We show the calculation for both.* Given: - Principal (P\displaystyle P) = Rs. 3,00,000\displaystyle \text{Rs. }3,00,000 - Time (t\displaystyle t) = 2\displaystyle 2 years - Difference between Compound Interest and Simple Interest (CI−SI\displaystyle CI - SI) = Rs. 2,400\displaystyle \text{Rs. }2,400 **Step 1: Use the difference formula for 2 years** Difference=P(r100)2\text{Difference} = P \left(\frac{r}{100}\right)^2 2400=300000(r100)22400 = 300000 \left(\frac{r}{100}\right)^2 2400=30r22400 = 30 r^2 r2=240030=80  ⟹  r=80≈8.94%r^2 = \frac{2400}{30} = 80 \implies r = \sqrt{80} \approx 8.94\% *(If the Principal was Rs. 3,75,000: 2400=3750r2/100  ⟹  r2=64  ⟹  r=8%\displaystyle 2400 = 3750 r^2 / 100 \implies r^2 = 64 \implies r = 8\%. This matches Option D.)* Hence, **Option D** is the correct answer.

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