Mathematics of FinanceMCQPYQ Sep 24Question 1267 of 512
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The compound interest on 40,000\displaystyle 40,000 at 12%\displaystyle 12\% per annum compounded quarterly for 6\displaystyle 6 months is:

Options

A2,463\displaystyle 2,463
B2,643\displaystyle 2,643
C2,364\displaystyle 2,364
D2,436\displaystyle 2,436
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Correct Answer

Option d2,436\displaystyle 2,436

All Options:

  • A2,463\displaystyle 2,463
  • B2,643\displaystyle 2,643
  • C2,364\displaystyle 2,364
  • D2,436\displaystyle 2,436

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Detailed Solution & Explanation

**Derivation of Compound Interest** Given: - Principal (P\displaystyle P) = Rs. 40,000\displaystyle \text{Rs. }40,000 - Nominal Rate (r\displaystyle r) = 12%\displaystyle 12\% per annum compounded quarterly - Time (t\displaystyle t) = 6\displaystyle 6 months = 0.5\displaystyle 0.5 years **Step 1: Find periodic rate (i\displaystyle i) and compounding periods (n\displaystyle n)** - Periodic rate i=r4=12%4=3%=0.03\displaystyle i = \frac{r}{4} = \frac{12\%}{4} = 3\% = 0.03 per quarter. - Number of quarters n=t×4=0.5×4=2\displaystyle n = t \times 4 = 0.5 \times 4 = 2 quarters. **Step 2: Calculate Future Value (A\displaystyle A) and Compound Interest (CI\displaystyle CI)** A=P(1+i)nA = P(1 + i)^n A=40000(1+0.03)2A = 40000(1 + 0.03)^2 A=40000(1.0609)=Rs. 42,436A = 40000(1.0609) = \text{Rs. }42,436 CI=AP=4243640000=Rs. 2,436CI = A - P = 42436 - 40000 = \text{Rs. }2,436 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

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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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