Mathematics of FinanceMCQPYQ 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 d8%\displaystyle 8\%

All Options:

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

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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 (CISI\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=808.94%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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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