What is the NPV of an investment into NFT, if it was bought today for $700 and is projected to be resold in 9 months for $20,000? Assume the cost of capital is 8% with continuous compounding.

Question

BlackTom AI · Accepted Answer

Continuous compounding discount uses PV = FV · e^(–rt), so begin by discounting the $20,000 resale value back 9 months (0.75 years) at 8% continuous rate and then subtract the purchase cost to get NPV.

1) Relevant knowledge points and formulas
- For continuous compounding, present value (PV) of a future amount FV received at time t years is PV = FV · e^(–r t).
- Net present value (NPV) = PV of future cash inflows − initial cash outflow (purchase cost).

2) Step-by-step reasoning
- Convert 9 months to years: t = 9/12 = 0.75 years.
- Use r = 8% = 0.08 (continuous).
- Compute PV of the resale: PV = 20,000 · e^(–0.08 × 0.75) = 20,000 · e^(–0.06).
- Subtract the initial cost of $700 to get NPV.

3) Calculations with intermediate steps
- Exponent: –r t = –0.08 × 0.75 = –0.06.
- e^(–0.06) ≈ 0.9417645336 (using the exponential function).
- PV = 20,000 × 0.9417645336 ≈ 18,835.290672.
- NPV = PV − initial cost = 18,835.290672 − 700 = 18,135.290672.
- Rounded to cents: $18,135.29.

4) Why this answer is correct
- The calculation correctly applies continuous discounting for the exact time horizon (0.75 years) and then deducts the initial outlay. That yields the present economic value of purchasing the NFT today and reselling in 9 months, net of the purchase price.

5) Why the other multiple-choice options are incorrect
- $18,146.45 and $18,903.97 likely arise from arithmetic or rounding mistakes or from using an incorrect discount factor (e.g., using a slightly different exponent or mis-subtracting the purchase cost).
- $18,907.84 corresponds to a different discounting assumption (for example, using a smaller effective discount or failing to subtract the $700), so it does not match continuous discounting as specified.

6) Conclusion
- Therefore, the NPV is $18,135.29, which matches the provided correct answer.

What is the NPV of an investment into NFT, if it was bought today for $700 and is projected to be resold in 9 months for $20,000? Assume the cost of capital is 8% with continuous compounding.单项选择题

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