Mathematics for FinancePYQ Jan. 21Question 1446 of 512
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₹800\displaystyle ₹ 800 is invested at the end of each month in an account paying interest 5%\displaystyle 5\% per year compounded monthly. What is the future value of this annuity after 10th\displaystyle 10^{th} payment?

Options

A₹4,444\displaystyle ₹ 4,444
B8,756\displaystyle 8,756
C3,491\displaystyle 3,491
D8,151.67\displaystyle 8,151.67
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Correct Answer

✅ Option d — 8,151.67\displaystyle 8,151.67

All Options:

  • A₹4,444\displaystyle ₹ 4,444
  • B8,756\displaystyle 8,756
  • C3,491\displaystyle 3,491
  • D8,151.67\displaystyle 8,151.67

Detailed Solution & Explanation

Let the monthly payment be A=Rs. 800\displaystyle A = \text{Rs. }800. Given parameters: * Nominal Interest Rate (r\displaystyle r) = 5%\displaystyle 5\% p.a. * Compounding Frequency (m\displaystyle m) = 12\displaystyle 12 * Monthly Interest Rate (i\displaystyle i) = 5%12≈0.0041667\displaystyle \frac{5\%}{12} \approx 0.0041667 * Number of payments (n\displaystyle n) = 10\displaystyle 10 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=800×(1.0041667)10−10.0041667FV = 800 \times \frac{(1.0041667)^{10} - 1}{0.0041667} First, let's calculate (1.0041667)10\displaystyle (1.0041667)^{10}: (1.0041667)10≈1.04253(1.0041667)^{10} \approx 1.04253 Now substitute this back: FV≈800×1.04253−10.0041667FV \approx 800 \times \frac{1.04253 - 1}{0.0041667} FV≈800×10.2072=8,165.76FV \approx 800 \times 10.2072 = 8,165.76 The closest option listed is Option D (8,151.67\displaystyle 8,151.67). Hence, **Option D** is the correct answer.

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