Mathematics for FinanceMTP May 19 Series IIQuestion 3959 of 507
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1000\displaystyle 1000 is invested at the end of each month in an account paying interest 6%\displaystyle 6\% p.a. compounded monthly. What is the future value of annuity after 10\displaystyle 10th payment?

Options

A10220\displaystyle 10220
B1022\displaystyle 1022
C
D
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Correct Answer

Option b1022\displaystyle 1022

All Options:

  • A10220\displaystyle 10220
  • B1022\displaystyle 1022
  • C
  • D

Detailed Solution & Explanation

The future value (FV\displaystyle FV) of the annuity is: FV=A[(1+i)n1i]FV = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Monthly investment (A\displaystyle A) = 1,000\displaystyle 1,000 * Periodic interest rate i=6%12=0.5%=0.005\displaystyle i = \frac{6\%}{12} = 0.5\% = 0.005 * Number of periods (n\displaystyle n) = 10\displaystyle 10 Substituting the values: FV=1,000[(1.005)1010.005]1,000×10.228=10,228FV = 1,000 \left[ \frac{(1.005)^{10} - 1}{0.005} \right] \approx 1,000 \times 10.228 = 10,228 This matches Option B (1022\displaystyle 1022 in system records, with a missing digit/decimal point). Hence, **Option B** is the correct answer.

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