Mathematics for FinanceMTP May 19Question 1494 of 512
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200\displaystyle 200 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 10\displaystyle 10th payment?

Options

A2045\displaystyle 2045
B2055\displaystyle 2055
C2044\displaystyle 2044
D2065\displaystyle 2065
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Correct Answer

✅ Option a — 2045\displaystyle 2045

All Options:

  • A2045\displaystyle 2045
  • B2055\displaystyle 2055
  • C2044\displaystyle 2044
  • D2065\displaystyle 2065

Detailed Solution & Explanation

The future value (FV\displaystyle FV) of an ordinary annuity compounded monthly is: FV=A[(1+i)n−1i]FV = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Monthly payment (A\displaystyle A) = 200\displaystyle 200 * Nominal interest rate (r\displaystyle r) = 6%\displaystyle 6\% p.a. * Periodic interest rate i=6%12=0.5%=0.005\displaystyle i = \frac{6\%}{12} = 0.5\% = 0.005 * Number of payments (n\displaystyle n) = 10\displaystyle 10 Substituting the values: FV=200[(1.005)10−10.005]FV = 200 \left[ \frac{(1.005)^{10} - 1}{0.005} \right] Using (1.005)10≈1.05114\displaystyle (1.005)^{10} \approx 1.05114: FV=200[1.05114−10.005]=200×10.228=2,045.60FV = 200 \left[ \frac{1.05114 - 1}{0.005} \right] = 200 \times 10.228 = 2,045.60 Thus, the future value is approximately 2,045\displaystyle 2,045. Hence, **Option A** is the correct answer.

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