Mathematics for FinanceMTP Dec 23 Series IIQuestion 1528 of 512
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Find the future value of an annuity of 500\displaystyle 500 is made annually for 7\displaystyle 7 years at interest rate of 14%\displaystyle 14\% compounded annually. [(1.14)7=2.5023]\displaystyle [(1.14)^7 = 2.5023]

Options

A5365.25\displaystyle 5365.25
B5265.25\displaystyle 5265.25
C5465.25\displaystyle 5465.25
DNone of these
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Correct Answer

✅ Option a — 5365.25\displaystyle 5365.25

All Options:

  • A5365.25\displaystyle 5365.25
  • B5265.25\displaystyle 5265.25
  • C5465.25\displaystyle 5465.25
  • DNone of these

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) = 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 * Given factor (1.14)7=2.5023\displaystyle (1.14)^7 = 2.5023 Substituting the values: FV=500[2.5023−10.14]≈5,365.36FV = 500 \left[ \frac{2.5023 - 1}{0.14} \right] \approx 5,365.36 This is closest to Option A (5365.25\displaystyle 5365.25). Hence, **Option A** is the correct answer.

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