Mathematics for FinancePYQ Dec 22Question 1458 of 512
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How much amount is required to be invested every year so as to accumulate ₹5,00,000\displaystyle ₹ 5,00,000 at the end of 12\displaystyle 12 years if interest is compounded annually at 10%\displaystyle 10\% p.a (1.12,0.1)=21.384281\displaystyle (1.12, 0.1) = 21.384281

Options

A₹23381.65\displaystyle ₹ 23381.65
B₹24385.85\displaystyle ₹ 24385.85
C₹26381.65\displaystyle ₹ 26381.65
D₹28362.75\displaystyle ₹ 28362.75
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Correct Answer

✅ Option a — ₹23381.65\displaystyle ₹ 23381.65

All Options:

  • A₹23381.65\displaystyle ₹ 23381.65
  • B₹24385.85\displaystyle ₹ 24385.85
  • C₹26381.65\displaystyle ₹ 26381.65
  • D₹28362.75\displaystyle ₹ 28362.75

Detailed Solution & Explanation

Let the annual investment be A\displaystyle A. Given parameters: * Target Future Value (FV\displaystyle FV) = Rs. 5,00,000\displaystyle \text{Rs. }5,00,000 * Time (n\displaystyle n) = 12\displaystyle 12 years * Interest Rate (r\displaystyle r) = 10%\displaystyle 10\% p.a., so i=0.10\displaystyle i = 0.10 * Given factor (1.10)12\displaystyle (1.10)^{12} cumulative growth factor (or FVIFA(12,0.10)\displaystyle FVIFA(12, 0.10)) = 21.384281\displaystyle 21.384281 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: 5,00,000=A×21.3842815,00,000 = A \times 21.384281 Solving for A\displaystyle A: A=5,00,00021.384281≈23,381.65A = \frac{5,00,000}{21.384281} \approx 23,381.65 Thus, the annual investment is approximately Rs. 23,381.65\displaystyle \text{Rs. }23,381.65. Hence, **Option A** is the correct answer.

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