Mathematics for FinancePYQ July 21Question 1450 of 512
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The future value of annuity of ₹2,000\displaystyle ₹ 2,000 for 5\displaystyle 5 years at 5%\displaystyle 5\% compounded annually is given as:

Options

A51,051\displaystyle 51,051
B21,021\displaystyle 21,021
C11,051\displaystyle 11,051
D61,054\displaystyle 61,054
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Correct Answer

✅ Option c — 11,051\displaystyle 11,051

All Options:

  • A51,051\displaystyle 51,051
  • B21,021\displaystyle 21,021
  • C11,051\displaystyle 11,051
  • D61,054\displaystyle 61,054

Detailed Solution & Explanation

Let the annual payment of the annuity be A=Rs. 2,000\displaystyle A = \text{Rs. }2,000. Given parameters: * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest Rate (r\displaystyle r) = 5%\displaystyle 5\% p.a., so i=0.05\displaystyle i = 0.05 The formula for the Future Value of an ordinary annuity is: FV=A×(1+i)n−1iFV = A \times \frac{(1+i)^n - 1}{i} Substituting the values: FV=2,000×(1.05)5−10.05FV = 2,000 \times \frac{(1.05)^5 - 1}{0.05} FV=2,000×1.27628−10.05FV = 2,000 \times \frac{1.27628 - 1}{0.05} FV=2,000×0.276280.05FV = 2,000 \times \frac{0.27628}{0.05} FV=2,000×5.5256=11,051.2FV = 2,000 \times 5.5256 = 11,051.2 Thus, the future value is approximately Rs. 11,051\displaystyle \text{Rs. }11,051. Hence, **Option C** is the correct answer.

Key Concepts to Understand

Annuity

A sequence of equal periodic payments made at equal intervals of time.

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