Mathematics for FinancePYQ Dec. 21Question 1451 of 512
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Mr. X wants to accumulate ₹50,00,000\displaystyle ₹ 50,00,000 at the end of 10\displaystyle 10 years. Then how much amount is required to be invested every year if interest is compounded annually at 10%\displaystyle 10\%? (Given that P(10,0.10)=15.9374298)\displaystyle P(10,0.10) = 15.9374298)

Options

A₹3,13,736.87\displaystyle ₹ 3,13,736.87
B₹4,13,726.87\displaystyle ₹ 4,13,726.87
C₹3,53,726.87\displaystyle ₹ 3,53,726.87
D₹4,53,726.87\displaystyle ₹ 4,53,726.87
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Correct Answer

✅ Option a — ₹3,13,736.87\displaystyle ₹ 3,13,736.87

All Options:

  • A₹3,13,736.87\displaystyle ₹ 3,13,736.87
  • B₹4,13,726.87\displaystyle ₹ 4,13,726.87
  • C₹3,53,726.87\displaystyle ₹ 3,53,726.87
  • D₹4,53,726.87\displaystyle ₹ 4,53,726.87

Detailed Solution & Explanation

Let the amount to be invested every year be A\displaystyle A. Given parameters: * Target Future Value (FV\displaystyle FV) = Rs. 50,00,000\displaystyle \text{Rs. }50,00,000 * Time (n\displaystyle n) = 10\displaystyle 10 years * Interest Rate (r\displaystyle r) = 10%\displaystyle 10\% p.a. compounded annually, so i=0.10\displaystyle i = 0.10 * Future Value Annuity Factor (FVIFA(10,0.10)\displaystyle FVIFA(10, 0.10)) ≈15.9374298\displaystyle \approx 15.9374298 The formula for the Future Value of an ordinary annuity is: FV=A×FVIFA(n,i)FV = A \times FVIFA(n, i) Substituting the values: 50,00,000=A×15.937429850,00,000 = A \times 15.9374298 Solving for A\displaystyle A: A=50,00,00015.9374298≈3,13,726.87A = \frac{50,00,000}{15.9374298} \approx 3,13,726.87 Thus, the amount required to be invested is approximately Rs. 3,13,726.87\displaystyle \text{Rs. }3,13,726.87. Hence, **Option A** is the correct answer.

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