Mathematics of FinanceMCQPYQ June 22Question 1454 of 512
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200\displaystyle ₹ 200 is invested at the end of each month in an account paying interest 6%\displaystyle 6\% per year compounded monthly. What is the future value of this annuity after 10th\displaystyle 10^{th} payment?

Options

A2,044\displaystyle 2,044
B12,044\displaystyle 12,044
C2,040\displaystyle 2,040
D12,000\displaystyle 12,000
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Correct Answer

Option a2,044\displaystyle 2,044

All Options:

  • A2,044\displaystyle 2,044
  • B12,044\displaystyle 12,044
  • C2,040\displaystyle 2,040
  • D12,000\displaystyle 12,000

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Detailed Solution & Explanation

Let the monthly payment be A=Rs. 200\displaystyle A = \text{Rs. }200. Given parameters: * Nominal Interest Rate (r\displaystyle r) = 6%\displaystyle 6\% p.a. * Compounding Frequency (m\displaystyle m) = 12\displaystyle 12 * Monthly Interest Rate (i\displaystyle i) = 6%12=0.5%=0.005\displaystyle \frac{6\%}{12} = 0.5\% = 0.005 * Number of payments (n\displaystyle n) = 10\displaystyle 10 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=200×(1.005)1010.005FV = 200 \times \frac{(1.005)^{10} - 1}{0.005} First, let's calculate (1.005)10\displaystyle (1.005)^{10}: (1.005)101.051140(1.005)^{10} \approx 1.051140 Now substitute this back: FV=200×1.05114010.005FV = 200 \times \frac{1.051140 - 1}{0.005} FV=200×10.228=2,045.60FV = 200 \times 10.228 = 2,045.60 The closest option listed is Option A (Rs. 2,044\displaystyle \text{Rs. }2,044). 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

Exam Strategy Tip

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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