Mathematics of FinanceMCQPYQ Nov. 20Question 1442 of 512
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A person decides to invest 1,25,000\displaystyle ₹ 1,25,000 per year for the next five years in an annuity which gives 5%\displaystyle 5\% p.a. compounded annually. What is the approx. future value? [(1.05)5=1.2762]\displaystyle [(1.05)^5 = 1.2762]

Options

A7,59,535\displaystyle 7,59,535
B6,90,500\displaystyle 6,90,500
C5,90,704\displaystyle 5,90,704
D3,59,535\displaystyle 3,59,535
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Correct Answer

Option b6,90,500\displaystyle 6,90,500

All Options:

  • A7,59,535\displaystyle 7,59,535
  • B6,90,500\displaystyle 6,90,500
  • C5,90,704\displaystyle 5,90,704
  • D3,59,535\displaystyle 3,59,535

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Detailed Solution & Explanation

Let the annual payment be A=Rs. 1,25,000\displaystyle A = \text{Rs. }1,25,000. Given parameters: * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest Rate (r\displaystyle r) = 5%\displaystyle 5\% p.a., so i=0.05\displaystyle i = 0.05 * Given factor: (1.05)5=1.27628\displaystyle (1.05)^5 = 1.27628 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=1,25,000×(1.05)510.05FV = 1,25,000 \times \frac{(1.05)^5 - 1}{0.05} FV=1,25,000×1.2762810.05FV = 1,25,000 \times \frac{1.27628 - 1}{0.05} FV=1,25,000×0.276280.05FV = 1,25,000 \times \frac{0.27628}{0.05} FV=1,25,000×5.5256=6,90,700FV = 1,25,000 \times 5.5256 = 6,90,700 Thus, the approximate future value is Rs. 6,90,500\displaystyle \text{Rs. }6,90,500 (Option B, using rounded textbook values). Hence, **Option B** 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.

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