Question13 Suppose you receive $1,100 per year for 5 years, starting with your first payment at the end of year 1, earning a return of 6.5%. What is the FV of these cash flows approximately equal to?Select one alternative: $4,571 $10,392 $6,263 $14,441 ResetMaximum marks: 3 Flag question undefined单项选择题
A
$4,571
B
$10,392
C
$6,263
D
$14,441

Question

Question13 Suppose you receive $1,100 per year for 5 years, starting with your first payment at the end of year 1, earning a return of 6.5%. What is the FV of these cash flows approximately equal to?Select one alternative: $4,571 $10,392 $6,263 $14,441 ResetMaximum marks: 3 Flag question undefined单项选择题

A

$4,571

B

$10,392

C

$6,263

D

$14,441

BlackTom AI · Accepted Answer

Future value of an ordinary annuity (payments at end of each period) is given by FV = PMT * [((1 + r)^n - 1) / r].

Knowledge points:
- PMT = $1,100, r = 0.065 (6.5%), n = 5.
- Use the annuity FV formula for end-of-year payments.

Step-by-step calculation:
1. Compute (1 + r)^n = 1.065^5. Calculate iteratively:
   - 1.065^2 = 1.134225
   - 1.065^3 = 1.134225 × 1.065 = 1.207949625
   - 1.065^4 = 1.207949625 × 1.065 = 1.286465850625
   - 1.065^5 = 1.286465850625 × 1.065 = 1.370086663415625 (rounded ≈ 1.3700866634)
2. Subtract 1: (1.065^5 − 1) = 0.370086663415625
3. Divide by r: 0.370086663415625 / 0.065 = 5.693640207940384 (≈ 5.693640208)
4. Multiply by PMT: FV = 1,100 × 5.693640208 = 6,263.004228 (≈ $6,263)

Why this answer is correct:
- The formula and arithmetic show the future value of five $1,100 end-of-year payments at 6.5% accumulates to about $6,263. This is slightly above the nominal sum of payments (5 × $1,100 = $5,500) because each payment earns interest for some years.

Why the other options are incorrect:
- $4,571 is less than the sum of payments ($5,500) and so cannot be the FV when interest is positive.
- $10,392 and $14,441 are much larger than the correct accumulation; they would require a much higher interest rate or more periods.

Conclusion: The calculated FV ≈ $6,263, which matches the provided correct answer $6,263.

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