Mathematics of FinanceMCQPYQ 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)×(10.08)\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)×(10.08)\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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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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

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