Mathematics of FinanceMCQMTP Dec 23 Series IQuestion 1393 of 512
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The Compounded interest Rs.8000\displaystyle 8000 for 6\displaystyle 6 months at 12%\displaystyle 12\% p.a payable quarterly is

Options

ARs.487.20\displaystyle 487.20
BRs.480\displaystyle 480
CRs.380\displaystyle 380
DNone of these
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Correct Answer

Option aRs.487.20\displaystyle 487.20

All Options:

  • ARs.487.20\displaystyle 487.20
  • BRs.480\displaystyle 480
  • CRs.380\displaystyle 380
  • DNone of these

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Detailed Solution & Explanation

**Derivation of Compound Interest** Given: - Principal (P\displaystyle P) = Rs. 8,000\displaystyle \text{Rs. }8,000 - Nominal rate (r\displaystyle r) = 12%\displaystyle 12\% per annum - Compounding Frequency = Payable quarterly (m=4\displaystyle m = 4) - Time (t\displaystyle t) = 6\displaystyle 6 months = 0.5\displaystyle 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 = \frac{r}{4} = \frac{12\%}{4} = 3\% = 0.03 - Total compounding periods n=t×4=0.5×4=2\displaystyle n = t \times 4 = 0.5 \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 \times 1.0609 = \text{Rs. }8,487.20 **Step 3: Calculate the Compound Interest (CI\displaystyle CI)** CI=AP=8487.208000=Rs. 487.20CI = A - P = 8487.20 - 8000 = \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

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