Mathematics of FinanceMCQMTP Dec 23 Series IQuestion 1393 of 512
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The Compounded interest Rs.$8000for\displaystyle for6\displaystyle months at $12\% p.a payable quarterly is

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

✅ Option a — Rs.$487.20$

All Options:

  • ARs.$487.20$
  • BRs.$480$
  • CRs.$380$
  • DNone of these

Detailed Solution & Explanation

**Derivation of Compound Interest** Given: - Principal (P\displaystyle P) = Rs. 8,000\displaystyle Rs. \displaystyle \text{Rs. }8,000 - Nominal rate (r\displaystyle r) = $12\%$ per annum - Compounding Frequency = Payable quarterly (m=4\displaystyle m = 4) - Time (t\displaystyle t) = 6\displaystyle 6 months = $0.5$ years **Step 1: Calculate periodic rate (i\displaystyle i) and total compounding periods (n\displaystyle n)** - Periodic rate i=r4=12%4=3%=0.03\displaystyle i = \displaystyle \frac{r}{4} = \frac{12\%}{4} = 3\% = 0.03 - Total compounding periods n=t×4=0.5×4=2\displaystyle n = t ×\displaystyle \times 4 = 0.5 ×\displaystyle \times 4 = 2 quarters **Step 2: Calculate the future value (A\displaystyle A)** A=P(1+i)nA = P(1 + i)^n A=8000(1+0.03)2A = 8000(1 + 0.03)^2 A=8000(1.03)2A = 8000(1.03)^2 A=8000×1.0609=Rs. 8,487.20A = 8000 ×\displaystyle \times 1.0609 = Rs. \displaystyle \text{Rs. }8,487.20 **Step 3: Calculate the Compound Interest (CI\displaystyle CI)** CI=A−P=8487.20−8000=Rs. 487.20CI = A - P = 8487.20 - 8000 = Rs. \displaystyle \text{Rs. }487.20 Hence, **Option A** 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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