Mathematics of FinanceMCQMTP Sep 24 Series IQuestion 3957 of 512
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The Compound interest 8000\displaystyle 8000 for 6\displaystyle 6 months at 12%\displaystyle 12\% p.a payable quarterly is:

Options

A487.20\displaystyle 487.20
B480\displaystyle 480
C380\displaystyle 380
DNone of these
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Correct Answer

Option a487.20\displaystyle 487.20

All Options:

  • A487.20\displaystyle 487.20
  • B480\displaystyle 480
  • C380\displaystyle 380
  • DNone of these

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Detailed Solution & Explanation

Given parameters: * Principal (P\displaystyle P) = Rs. 8,000\displaystyle \text{Rs. }8,000 * Nominal Interest Rate (r\displaystyle r) = 12%\displaystyle 12\% p.a. * Time (t\displaystyle t) = 6\displaystyle 6 months = 0.5\displaystyle 0.5 years Since the interest is compounded quarterly: * Number of conversion periods per year (m\displaystyle m) = 4\displaystyle 4 * Quarterly interest rate (i\displaystyle i) = 12%4=3%=0.03\displaystyle \frac{12\%}{4} = 3\% = 0.03 * Total number of conversion periods (n\displaystyle n) = t×m=0.5×4=2\displaystyle t \times m = 0.5 \times 4 = 2 quarters The formula for compound amount is: A=P(1+i)nA = P(1+i)^n Substituting the values: A=8,000×(1.03)2A = 8,000 \times (1.03)^2 A=8,000×1.0609=8,487.20A = 8,000 \times 1.0609 = 8,487.20 The Compound Interest (CI\displaystyle CI) is: CI=AP=8,487.208,000=487.20CI = A - P = 8,487.20 - 8,000 = 487.20 Thus, the compound interest is Rs. 487.20\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.

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