Mathematics for FinanceMTP June 24 Series IQuestion 1530 of 512
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The future value of an annuity of 1500\displaystyle 1500 made annually for 5\displaystyle 5 years at an interest rate of 10%\displaystyle 10\% compounded annually is

Options

A9517.56\displaystyle 9517.56
B9157.65\displaystyle 9157.65
C9715.36\displaystyle 9715.36
D9175.65\displaystyle 9175.65
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Correct Answer

✅ Option b — 9157.65\displaystyle 9157.65

All Options:

  • A9517.56\displaystyle 9517.56
  • B9157.65\displaystyle 9157.65
  • C9715.36\displaystyle 9715.36
  • D9175.65\displaystyle 9175.65

Detailed Solution & Explanation

The future value (FV\displaystyle FV) of the annuity is: FV=A[(1+i)n−1i]FV = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Annual investment (A\displaystyle A) = 1,500\displaystyle 1,500 * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest rate (i\displaystyle i) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 Substituting the values: FV=1,500[(1.10)5−10.10]FV = 1,500 \left[ \frac{(1.10)^5 - 1}{0.10} \right] Using (1.10)5=1.61051\displaystyle (1.10)^5 = 1.61051: FV=1,500×6.1051=9,157.65FV = 1,500 \times 6.1051 = 9,157.65 This matches Option B (9157.65\displaystyle 9157.65). Hence, **Option B** is the correct answer.

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