Mathematics for FinancePYQ June 22Question 1454 of 512
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₹200\displaystyle ₹ 200 is invested at the end of each month in an account paying interest 6%\displaystyle 6\% per year compounded monthly. What is the future value of this annuity after 10th\displaystyle 10^{th} payment?

Options

A2,044\displaystyle 2,044
B12,044\displaystyle 12,044
C2,040\displaystyle 2,040
D12,000\displaystyle 12,000
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Correct Answer

✅ Option a — 2,044\displaystyle 2,044

All Options:

  • A2,044\displaystyle 2,044
  • B12,044\displaystyle 12,044
  • C2,040\displaystyle 2,040
  • D12,000\displaystyle 12,000

Detailed Solution & Explanation

Let the monthly payment be A=Rs. 200\displaystyle A = \text{Rs. }200. Given parameters: * Nominal Interest Rate (r\displaystyle r) = 6%\displaystyle 6\% p.a. * Compounding Frequency (m\displaystyle m) = 12\displaystyle 12 * Monthly Interest Rate (i\displaystyle i) = 6%12=0.5%=0.005\displaystyle \frac{6\%}{12} = 0.5\% = 0.005 * 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=200×(1.005)10−10.005FV = 200 \times \frac{(1.005)^{10} - 1}{0.005} First, let's calculate (1.005)10\displaystyle (1.005)^{10}: (1.005)10≈1.051140(1.005)^{10} \approx 1.051140 Now substitute this back: FV=200×1.051140−10.005FV = 200 \times \frac{1.051140 - 1}{0.005} FV=200×10.228=2,045.60FV = 200 \times 10.228 = 2,045.60 The closest option listed is Option A (Rs. 2,044\displaystyle \text{Rs. }2,044). Hence, **Option A** is the correct answer.

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