Question11 Present value (single sum): You will receive $9,000 in 4 years; r = 6%. The PV ≈ ?Select one alternative: $7,129 $6,840 $8,491 $7,000 ResetMaximum marks: 3 Flag question undefined单项选择题
A
$7,129
B
$6,840
C
$8,491
D
$7,000

Question

Question11 Present value (single sum): You will receive $9,000 in 4 years; r = 6%. The PV ≈ ?Select one alternative: $7,129 $6,840 $8,491 $7,000 ResetMaximum marks: 3 Flag question undefined

BlackTom AI · Accepted Answer

Present value of a single future sum is computed with PV = FV / (1 + r)^n.

1) Relevant concepts:
- FV (future value) = $9,000, r (annual discount rate) = 6% = 0.06, n (number of years) = 4.
- Discounting a future amount reduces it to its present equivalent by dividing by the compound growth factor (1 + r)^n.

2) Step-by-step reasoning and calculations:
- Compute the compound factor (1 + r)^n = (1.06)^4.
  - (1.06)^2 = 1.06 × 1.06 = 1.1236
  - (1.06)^3 = 1.1236 × 1.06 = 1.191016
  - (1.06)^4 = 1.191016 × 1.06 = 1.26247696
- Now compute PV = 9,000 / 1.26247696.

3) Intermediate arithmetic:
- 9,000 ÷ 1.26247696 ≈ 7,128.85 (carrying sufficient decimal places)
- Rounding to the nearest dollar gives PV ≈ $7,129.

4) Why this is correct:
- The calculation follows the standard present-value formula for a single future sum and uses exact compounding for four years at 6%. The divisor 1.26247696 correctly reflects four years of 6% growth, so dividing $9,000 by that factor yields the present-equivalent value.

5) Why the other choices are incorrect:
- $6,840 implies a larger discount factor (9,000/6,840 ≈ 1.3158) which would correspond to a higher effective rate or longer period than 6% for 4 years.
- $8,491 implies a much smaller discount factor (9,000/8,491 ≈ 1.0599), essentially only about one year of 6% discounting, not four.
- $7,000 is slightly lower than the correct PV; it corresponds to a discount factor of about 1.2857, again larger than the correct 1.2625, so it underestimates the PV.

6) Conclusion:
The present value of $9,000 received in 4 years at r = 6% is approximately $7,129, which matches the provided correct answer $7,129.

Question11 Present value (single sum): You will receive $9,000 in 4 years; r = 6%. The PV ≈ ?Select one alternative: $7,129 $6,840 $8,491 $7,000 ResetMaximum marks: 3 Flag question undefined单项选择题

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