Mathematics for FinancePYQ Sep 24Question 1481 of 512
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In an account paying interest @9%\displaystyle @9\% per year compounded monthly, 200\displaystyle 200 is invested at the end of each month. What is the future value of this annuity after 10th\displaystyle 10^{th} payment? (Where (1.00/5)10=1.0775\displaystyle (1.00/5)^{10} = 1.0775 )

Options

A2,060\displaystyle 2,060
B2,022\displaystyle 2,022
C2,044\displaystyle 2,044
D2,155\displaystyle 2,155
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Correct Answer

✅ Option a — 2,060\displaystyle 2,060

All Options:

  • A2,060\displaystyle 2,060
  • B2,022\displaystyle 2,022
  • C2,044\displaystyle 2,044
  • D2,155\displaystyle 2,155

Detailed Solution & Explanation

The future value (FV\displaystyle FV) of an ordinary annuity 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) = 9%\displaystyle 9\% p.a. * Compounding frequency (m\displaystyle m) = 12\displaystyle 12 (monthly), so periodic interest rate i=9%12=0.75%=0.0075\displaystyle i = \frac{9\%}{12} = 0.75\% = 0.0075 * Number of payments (n\displaystyle n) = 10\displaystyle 10 * Given factor: (1.0075)10=1.0775\displaystyle (1.0075)^{10} = 1.0775 Substituting the values: FV=200[1.0775−10.0075]=200×0.07750.0075≈2066.67FV = 200 \left[ \frac{1.0775 - 1}{0.0075} \right] = 200 \times \frac{0.0775}{0.0075} \approx 2066.67 The calculated future value is approximately 2,066.67\displaystyle 2,066.67, which is closest to Option A (2,060\displaystyle 2,060 in system records). Hence, **Option A** is the correct answer.

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