Mathematics of FinanceMCQPYQ June 19Question 1437 of 512
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Let a person invest a fixed sum at the end of each month in an account paying interest $12\%\displaystyle per year compounded monthly. If the future value of this annuity after the $12^{th} payment is ₹55,000\displaystyle ₹ 55,000 then the amount invested every month is?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — ₹4,337\displaystyle ₹ 4,337

All Options:

  • A₹4,837\displaystyle ₹ 4,837
  • B₹4,637\displaystyle ₹ 4,637
  • C₹4,337\displaystyle ₹ 4,337
  • D₹3,337\displaystyle ₹ 3,337

Detailed Solution & Explanation

Let the fixed sum invested every month be A\displaystyle A. Given parameters: * Future Value of annuity (FV\displaystyle FV) = Rs. 55,000\displaystyle Rs. \displaystyle \text{Rs. }55,000 * Nominal Interest Rate (r\displaystyle r) = $12\%$ p.a. * Compounding Frequency (m\displaystyle m) = $12$ (compounded monthly) * Monthly Interest Rate (i\displaystyle i) = 12%12=1%=0.01\displaystyle 12%12=1\displaystyle \frac{12\%}{12} = 1\% = 0.01 * Number of payments (n\displaystyle n) = $12$ The formula for the Future Value of an ordinary annuity is: FV=A×(1+i)n−1iFV = A ×\displaystyle \times (1+i)n−1i\displaystyle \frac{(1+i)^n - 1}{i} Substituting the values: 55,000=A×(1.01)12−10.0155,000 = A ×\displaystyle \times (1.01)12−10.01\displaystyle \frac{(1.01)^{12} - 1}{0.01} First, let's calculate (1.01)12\displaystyle (1.01)^{12}: (1.01)12≈1.126825(1.01)^{12} ≈\displaystyle \approx 1.126825 Substituting this back: 55,000=A×1.126825−10.0155,000 = A ×\displaystyle \times 1.126825−10.01\displaystyle \frac{1.126825 - 1}{0.01} 55,000=A×0.1268250.0155,000 = A ×\displaystyle \times 0.1268250.01\displaystyle \frac{0.126825}{0.01} 55,000=12.6825A55,000 = 12.6825 A Solving for A\displaystyle A: A=55,00012.6825≈4,336.68A = 55,00012.6825\displaystyle \frac{55,000}{12.6825} ≈\displaystyle \approx 4,336.68 Thus, the monthly investment is approximately Rs. 4,337\displaystyle Rs. \displaystyle \text{Rs. }4,337. Hence, **Option C** 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.

Key Concepts to Understand

Annuity

A sequence of equal periodic payments made at equal intervals of time.

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