Mathematics for FinancePYQ Nov. 20Question 1441 of 512
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A five year annuity due has periodic cash flow of ₹100\displaystyle ₹ 100 each year. If the interest rate is 8%\displaystyle 8\% the future value of this annuity is given by:

Options

A₹(100)×(Future value at rate 8% for 5 years)×(1.08)\displaystyle ₹ (100) \times (\text{Future value at rate } 8\% \text{ for } 5 \text{ years}) \times (1.08)
B₹(100)×(Future value at rate 8% for 5 years)×(1−0.08)\displaystyle ₹ (100) \times (\text{Future value at rate } 8\% \text{ for } 5 \text{ years}) \times (1 - 0.08)
C₹(100)×(Future value at rate 8% for 5 years)×(1+0.08)\displaystyle ₹ (100) \times (\text{Future value at rate } 8\% \text{ for } 5 \text{ years}) \times (1 + 0.08)
D₹(100)×(Future value at rate 8% for 5 years)×(1/0.08)\displaystyle ₹ (100) \times (\text{Future value at rate } 8\% \text{ for } 5 \text{ years}) \times (1/0.08)
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Correct Answer

✅ Option c — ₹(100)×(Future value at rate 8% for 5 years)×(1+0.08)\displaystyle ₹ (100) \times (\text{Future value at rate } 8\% \text{ for } 5 \text{ years}) \times (1 + 0.08)

All Options:

  • A₹(100)×(Future value at rate 8% for 5 years)×(1.08)\displaystyle ₹ (100) \times (\text{Future value at rate } 8\% \text{ for } 5 \text{ years}) \times (1.08)
  • B₹(100)×(Future value at rate 8% for 5 years)×(1−0.08)\displaystyle ₹ (100) \times (\text{Future value at rate } 8\% \text{ for } 5 \text{ years}) \times (1 - 0.08)
  • C₹(100)×(Future value at rate 8% for 5 years)×(1+0.08)\displaystyle ₹ (100) \times (\text{Future value at rate } 8\% \text{ for } 5 \text{ years}) \times (1 + 0.08)
  • D₹(100)×(Future value at rate 8% for 5 years)×(1/0.08)\displaystyle ₹ (100) \times (\text{Future value at rate } 8\% \text{ for } 5 \text{ years}) \times (1/0.08)

Detailed Solution & Explanation

Let the periodic cash flow be C=Rs. 100\displaystyle C = \text{Rs. }100 and the interest rate be i=0.08\displaystyle i = 0.08. The time period is n=5\displaystyle n = 5 years. The future value of an ordinary annuity (payment at the end of each year) is given by: FVordinary=100×Future value interest factor at 8% for 5 yearsFV_{\text{ordinary}} = 100 \times \text{Future value interest factor at 8\% for 5 years} For an annuity due (periodic cash flow at the beginning of each year), the payments compound for one additional period. Thus, the Future Value of the annuity due (FVdue\displaystyle FV_{\text{due}}) is: FVdue=FVordinary×(1+i)FV_{\text{due}} = FV_{\text{ordinary}} \times (1 + i) FVdue=100×(Future value interest factor at 8% for 5 years)×(1+0.08)FV_{\text{due}} = 100 \times (\text{Future value interest factor at 8\% for 5 years}) \times (1 + 0.08) This matches Option C. Hence, **Option C** is the correct answer.

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