Mathematics of FinanceMCQPYQ Jan. 21Question 1445 of 512
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Find the future value of annuity of ₹1,000\displaystyle ₹ 1,000 made annually for 7\displaystyle 7 year at interest rate of $14\%$ compounded annually

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

✅ Option a — ₹10,730.7\displaystyle ₹ 10,730.7

All Options:

  • A₹10,730.7\displaystyle ₹ 10,730.7
  • B$5,365.35$
  • C$8,756$
  • D$9892.34$

Detailed Solution & Explanation

Let the annual payment of the annuity be A=Rs. 1,000\displaystyle A = Rs. \displaystyle \text{Rs. }1,000. Given parameters: * Time (n\displaystyle n) = 7\displaystyle 7 years * Interest Rate (r\displaystyle r) = $14\%p.a.,so\displaystyle p.a., soi = 0.14$ * Given factor: (1.14)7=2.5023\displaystyle (1.14)^7 = 2.5023 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: FV=1,000×(1.14)7−10.14FV = 1,000 ×\displaystyle \times (1.14)7−10.14\displaystyle \frac{(1.14)^7 - 1}{0.14} FV=1,000×2.5023−10.14FV = 1,000 ×\displaystyle \times 2.5023−10.14\displaystyle \frac{2.5023 - 1}{0.14} FV=1,000×1.50230.14FV = 1,000 ×\displaystyle \times 1.50230.14\displaystyle \frac{1.5023}{0.14} FV≈1,000×10.7307=10,730.7FV ≈\displaystyle \approx 1,000 ×\displaystyle \times 10.7307 = 10,730.7 Thus, the future value of the annuity is Rs. 10,730.7\displaystyle Rs. \displaystyle \text{Rs. }10,730.7. (Note: While some keys mark Option B, Option A is the mathematically correct value). 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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