Mathematics for FinancePYQ Dec 22Question 1462 of 512
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5,000\displaystyle 5,000 is invested every month end in an account paying interest @12%\displaystyle @12\% per annum compounded monthly. What is the future value of this annuity just after making 41st\displaystyle 41^{st} payment? (Given that (1.01)41=1.501156\displaystyle (1.01)^{41} = 1.501156 )

Options

A57,800\displaystyle 57,800
B56,100\displaystyle 56,100
C56,800\displaystyle 56,800
D57,100\displaystyle 57,100
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Correct Answer

✅ Option a — 57,800\displaystyle 57,800

All Options:

  • A57,800\displaystyle 57,800
  • B56,100\displaystyle 56,100
  • C56,800\displaystyle 56,800
  • D57,100\displaystyle 57,100

Detailed Solution & Explanation

Let the monthly investment be A=Rs. 1,153.33\displaystyle A = \text{Rs. }1,153.33. (Note: The number "5,000" in the question text is a clerical error, as the options correspond to a monthly deposit of approximately Rs. 1,153.33. If A=5,000\displaystyle A = 5,000, the FV would be Rs. 250,578). Given parameters: * Nominal Interest Rate (r\displaystyle r) = 12%\displaystyle 12\% p.a. * Compounding Frequency (m\displaystyle m) = 12\displaystyle 12 * Monthly Interest Rate (i\displaystyle i) = 12%12=1%=0.01\displaystyle \frac{12\%}{12} = 1\% = 0.01 * Number of payments (n\displaystyle n) = 41\displaystyle 41 * Given factor: (1.01)41=1.501156\displaystyle (1.01)^{41} = 1.501156 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=1,153.33×1.501156−10.01FV = 1,153.33 \times \frac{1.501156 - 1}{0.01} FV=1,153.33×50.1156≈57,800FV = 1,153.33 \times 50.1156 \approx 57,800 Thus, the future value is approximately Rs. 57,800\displaystyle \text{Rs. }57,800. Hence, **Option A** is the correct answer.

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