Mathematics of FinanceMCQPYQ June 22Question 1456 of 512
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Ankit invests 3,000\displaystyle ₹ 3,000 at the end of each quarter receiving interest @ 7%\displaystyle 7\% p.a. for 5\displaystyle 5 years. What amount will be receive at the end of the period?

Options

A71,200.20\displaystyle ₹ 71,200.20
B71,045.83\displaystyle ₹ 71,045.83
C73,204.83\displaystyle ₹ 73,204.83
DNone of these
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Correct Answer

Option b71,045.83\displaystyle ₹ 71,045.83

All Options:

  • A71,200.20\displaystyle ₹ 71,200.20
  • B71,045.83\displaystyle ₹ 71,045.83
  • C73,204.83\displaystyle ₹ 73,204.83
  • DNone of these

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Detailed Solution & Explanation

Let the quarterly payment be A=Rs. 3,000\displaystyle A = \text{Rs. }3,000. Given parameters: * Nominal Interest Rate (r\displaystyle r) = 7%\displaystyle 7\% p.a. * Compounding Frequency (m\displaystyle m) = 4\displaystyle 4 (compounded quarterly) * Quarterly Interest Rate (i\displaystyle i) = 7%4=1.75%=0.0175\displaystyle \frac{7\%}{4} = 1.75\% = 0.0175 * Time (t\displaystyle t) = 5\displaystyle 5 years, so n=5×4=20\displaystyle n = 5 \times 4 = 20 quarters The formula for the Future Value of an ordinary annuity is: FV=A×(1+i)n1iFV = A \times \frac{(1+i)^n - 1}{i} Substituting the values: FV=3,00,000×(1.0175)2010.0175FV = 3,00,000 \times \frac{(1.0175)^{20} - 1}{0.0175} Wait, the principal quarterly payment is Rs. 3,000. FV=3,000×(1.0175)2010.0175FV = 3,000 \times \frac{(1.0175)^{20} - 1}{0.0175} First, let's calculate (1.0175)20\displaystyle (1.0175)^{20}: (1.0175)201.414778(1.0175)^{20} \approx 1.414778 Now substitute this back: FV=3,000×1.41477810.0175FV = 3,000 \times \frac{1.414778 - 1}{0.0175} FV=3,000×23.7016=71,104.80FV = 3,000 \times 23.7016 = 71,104.80 The closest option listed is Option B (Rs. 71,045.83\displaystyle \text{Rs. }71,045.83). 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

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