Mathematics for FinancePYQ 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 b — 6,90,500\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

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)n−1iFV = A \times \frac{(1+i)^n - 1}{i} Substituting the values: FV=1,25,000×(1.05)5−10.05FV = 1,25,000 \times \frac{(1.05)^5 - 1}{0.05} FV=1,25,000×1.27628−10.05FV = 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.

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