Mathematics of FinanceMCQMTP Jun 23 Series IQuestion 1522 of 512
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$10,000$ is invested every month and in an account paying interest $@12\%\displaystyle per annum compounded monthly. What is the future value of this annuity just after making $11^{th} payment

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

✅ Option a — $115,600$

All Options:

  • A$115,600$
  • B$116,100$
  • C$156,800$
  • D$157,100$

Detailed Solution & Explanation

The future value (FV\displaystyle FV) of an ordinary annuity compounded monthly is: FV=A[(1+i)n−1i]FV = A \left[ (1+i)n−1i\displaystyle \frac{(1+i)^n - 1}{i} \right] Given: * Monthly investment (A\displaystyle A) = $10,000$ * Number of payments (n\displaystyle n) = $11$ * Nominal rate = $12\%$ p.a., so periodic rate $i = 12%12=1\displaystyle \frac{12\%}{12} = 1\% = 0.01$ Substituting the values: FV=10,000[(1.01)11−10.01]FV = 10,000 \left[ (1.01)11−10.01\displaystyle \frac{(1.01)^{11} - 1}{0.01} \right] Using (1.01)11≈1.115668\displaystyle (1.01)^{11} ≈\displaystyle \approx 1.115668: FV=10,000[1.115668−10.01]=10,000×11.5668=1,15,668FV = 10,000 \left[ 1.115668−10.01\displaystyle \frac{1.115668 - 1}{0.01} \right] = 10,000 ×\displaystyle \times 11.5668 = 1,15,668 This is closest to Option A ($115,600$). 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.

Key Concepts to Understand

Annuity

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

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If Rs. 1,000\displaystyle Rs. \displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every $10$ years, then the number in years in which it will amount to $Rs. \displaystyle \text{Rs. }2,000$ is:

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