Mathematics of FinanceMCQPYQ Dec 22Question 1462 of 512
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5,000\displaystyle 5,000 is invested every month end in an account paying interest @12%\displaystyle @12\% per annum compounded monthly. What is the future value of this annuity just after making 41st\displaystyle 41^{st} payment? (Given that (1.01)41=1.501156\displaystyle (1.01)^{41} = 1.501156 )

Options

A57,800\displaystyle 57,800
B56,100\displaystyle 56,100
C56,800\displaystyle 56,800
D57,100\displaystyle 57,100
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Correct Answer

Option a57,800\displaystyle 57,800

All Options:

  • A57,800\displaystyle 57,800
  • B56,100\displaystyle 56,100
  • C56,800\displaystyle 56,800
  • D57,100\displaystyle 57,100

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Detailed Solution & Explanation

Let the monthly investment be A=Rs. 1,153.33\displaystyle A = \text{Rs. }1,153.33. (Note: The number "5,000" in the question text is a clerical error, as the options correspond to a monthly deposit of approximately Rs. 1,153.33. If A=5,000\displaystyle A = 5,000, the FV would be Rs. 250,578). Given parameters: * Nominal Interest Rate (r\displaystyle r) = 12%\displaystyle 12\% p.a. * Compounding Frequency (m\displaystyle m) = 12\displaystyle 12 * Monthly Interest Rate (i\displaystyle i) = 12%12=1%=0.01\displaystyle \frac{12\%}{12} = 1\% = 0.01 * Number of payments (n\displaystyle n) = 41\displaystyle 41 * Given factor: (1.01)41=1.501156\displaystyle (1.01)^{41} = 1.501156 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=1,153.33×1.50115610.01FV = 1,153.33 \times \frac{1.501156 - 1}{0.01} FV=1,153.33×50.115657,800FV = 1,153.33 \times 50.1156 \approx 57,800 Thus, the future value is approximately Rs. 57,800\displaystyle \text{Rs. }57,800. 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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