Mathematics of FinanceMCQPYQ Dec 22Question 1241 of 512
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The difference between compound interest and simple interest on an amount of $15,000for\displaystyle for2$ years is $96$. What is the rate of interest p.a.?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — 8%\displaystyle 8\%

All Options:

  • A9%\displaystyle 9\%
  • B8%\displaystyle 8\%
  • C$10\%$
  • D$11\%$

Detailed Solution & Explanation

**Derivation of Interest Rate from Interest Difference** Given: - Principal (P\displaystyle P) = Rs. 15,000\displaystyle Rs. \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 Rs. \displaystyle \text{Rs. }96 **Step 1: Use the difference formula for 2 years** Difference=P(r100)2Difference=P\displaystyle \text{Difference} = P \left(r100\displaystyle \frac{r}{100}\right)^2 96=15000(r100)296 = 15000 \left(r100\displaystyle \frac{r}{100}\right)^2 96=15000×r21000096 = 15000 ×\displaystyle \times r210000\displaystyle \frac{r^2}{10000} 96=1.5r296 = 1.5 r^2 **Step 2: Solve for r\displaystyle r** r2=961.5=64r^2 = 961.5=64\displaystyle \frac{96}{1.5} = 64 r=64=8% per annumr = 64=8\displaystyle \sqrt{64} = 8\%  per annum\displaystyle \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

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.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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