Mathematics for FinancePYQ Nov. 20Question 1440 of 512
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Find the present value of ₹1,00,000\displaystyle ₹ 1,00,000 to be required after 5\displaystyle 5 years if the interest rate be 9%\displaystyle 9\%. Given that (1.09)5=1.5386\displaystyle (1.09)^5 = 1.5386.

Options

A70,993.48\displaystyle 70,993.48
B64,994.15\displaystyle 64,994.15
C88,992.43\displaystyle 88,992.43
D93,902.12\displaystyle 93,902.12
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Correct Answer

✅ Option b — 64,994.15\displaystyle 64,994.15

All Options:

  • A70,993.48\displaystyle 70,993.48
  • B64,994.15\displaystyle 64,994.15
  • C88,992.43\displaystyle 88,992.43
  • D93,902.12\displaystyle 93,902.12

Detailed Solution & Explanation

Let the present value (the amount to be invested today) be PV\displaystyle PV. Given parameters: * Future Value (FV\displaystyle FV) = Rs. 1,00,000\displaystyle \text{Rs. }1,00,000 * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest Rate (r\displaystyle r) = 9%\displaystyle 9\% p.a., so i=0.09\displaystyle i = 0.09 * Given factor: (1.09)5=1.5386\displaystyle (1.09)^5 = 1.5386 The compound interest amount formula is: FV=PV×(1+i)nFV = PV \times (1+i)^n Substituting the values: 1,00,000=PV×(1.09)51,00,000 = PV \times (1.09)^5 1,00,000=PV×1.53861,00,000 = PV \times 1.5386 Solving for PV\displaystyle PV: PV=1,00,0001.5386≈64,994.15PV = \frac{1,00,000}{1.5386} \approx 64,994.15 Thus, the present value is approximately Rs. 64,994.15\displaystyle \text{Rs. }64,994.15. Hence, **Option B** is the correct answer.

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