Mathematics for FinanceMTP May 19 Series IIQuestion 1499 of 512
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The future value of annuity on 5000\displaystyle 5000 a year for 7\displaystyle 7 years at 14%\displaystyle 14\% per annum compounded interest is

Options

A53300\displaystyle 53300
B5365.87\displaystyle 5365.87
C5480\displaystyle 5480
D5465.23\displaystyle 5465.23
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Correct Answer

✅ Option b — 5365.87\displaystyle 5365.87

All Options:

  • A53300\displaystyle 53300
  • B5365.87\displaystyle 5365.87
  • C5480\displaystyle 5480
  • D5465.23\displaystyle 5465.23

Detailed Solution & Explanation

If the annual payment is A=500\displaystyle A = 500, the future value (FV\displaystyle FV) is: FV=A[(1+i)n−1i]FV = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Annual payment (A\displaystyle A) = 500\displaystyle 500 * Time (n\displaystyle n) = 7\displaystyle 7 years * Interest rate (i\displaystyle i) = 14%\displaystyle 14\% p.a. = 0.14\displaystyle 0.14 Substituting the values: FV=500[(1.14)7−10.14]≈500×10.7307=5,365.35FV = 500 \left[ \frac{(1.14)^7 - 1}{0.14} \right] \approx 500 \times 10.7307 = 5,365.35 This matches Option B (5365.87\displaystyle 5365.87). Hence, **Option B** is the correct answer.

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