Mathematics of FinanceMCQPYQ Dec 22Question 1241 of 512
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The difference between compound interest and simple interest on an amount of 15,000\displaystyle 15,000 for 2\displaystyle 2 years is 96\displaystyle 96. What is the rate of interest p.a.?

Options

A9%\displaystyle 9\%
B8%\displaystyle 8\%
C10%\displaystyle 10\%
D11%\displaystyle 11\%
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Correct Answer

Option b8%\displaystyle 8\%

All Options:

  • A9%\displaystyle 9\%
  • B8%\displaystyle 8\%
  • C10%\displaystyle 10\%
  • D11%\displaystyle 11\%

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Detailed Solution & Explanation

**Derivation of Interest Rate from Interest Difference** Given: - Principal (P\displaystyle P) = Rs. 15,000\displaystyle \text{Rs. }15,000 - Time (t\displaystyle t) = 2\displaystyle 2 years - Difference between Compound Interest (CI\displaystyle CI) and Simple Interest (SI\displaystyle SI) = Rs. 96\displaystyle \text{Rs. }96 **Step 1: Use the difference formula for 2 years** Difference=P(r100)2\text{Difference} = P \left(\frac{r}{100}\right)^2 96=15000(r100)296 = 15000 \left(\frac{r}{100}\right)^2 96=15000×r21000096 = 15000 \times \frac{r^2}{10000} 96=1.5r296 = 1.5 r^2 **Step 2: Solve for r\displaystyle r** r2=961.5=64r^2 = \frac{96}{1.5} = 64 r=64=8% per annumr = \sqrt{64} = 8\% \text{ per annum} Hence, **Option B** 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

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