What is the future value at the end of Year 5 for the following cash flow stream, assuming an interest rate of 5.0%?

Beginning of Year 1 = $5,000

Beginning of Year 2 = $20,000

End of Year 3 = $15,000

End of Year 5 = $20,000

Question

What is the future value at the end of Year 5 for the following cash flow stream, assuming an interest rate of 5.0%?

Beginning of Year 1 = $5,000

Beginning of Year 2 = $20,000

End of Year 3 = $15,000

End of Year 5 = $20,000

BlackTom AI · Accepted Answer

First, I restate the problem to ensure we’re calculating the future value at the end of Year 5 correctly. We have cash flows at different times: $5,000 at the beginning of Year 1 (t = 0), $20,000 at the beginning of Year 2 (t = 1), $15,000 at the end of Year 3 (t = 3), and $20,000 at the end of Year 5 (t = 5). The interest rate is 5% per year, and we want the value accumulated to t = 5.

Option A: $68.7973
To evaluate this, we’d need to check if the sum of accumulated cash flows to t = 5 equals about $68,797.30. This seems too high given the cash flows and the 5% rate; the contributions from earlier cash flows are not large enough to reach this level when accumulated for the remaining years. Specifically, the largest single accumulation is 20,000 from t = 1 to t = 5, which yields 20,000*(1.05)^4 ≈ 24,310.13, and the other pieces add much less. So this option is unlikely.

Option B: $69.0958
Similar to Option A, this would require the total accumulated value to be around $69,095.80. The math from the actual accumulations is lower than this, given the same cash flows and rate; the sum we compute will be in the low $60k’s, not $69k’s. This option is inconsistent with the standard accumulation calculations.

Option C: $66.3495
This value is also not aligning with the expected accumulation. If we sum the properly accumulated amounts to t = 5, we get a figure around $67,000 to $68,000 range, not $66,349.50. The number is too small relative to the proper compounding of the given cash flows, so this option is incorrect.

Option D: $67.2275
Now, let’s compute carefully to verify near this figure. Accumulate each cash flow to t = 5:
- $5,000 at t = 0 grows for 5 years: 5,000*(1.05)^5 ≈ 5,000*1.2762815625 ≈ 6,381.41
- $20,000 at t = 1 grows for 4 years: 20,000*(1.05)^4 ≈ 20,000*1.21550625 ≈ 24,310.13
- $15,000 at t = 3 grows for 2 years: 15,000*(1.05)^2 ≈ 15,000*1.1025 ≈ 16,537.50
- $20,000 at t = 5 has no growth: 20,000
Add them: 6,381.41 + 24,310.13 + 16,537.50 + 20,000 ≈ 67,229.04.
The resulting total is approximately $67,229.04, which is very close to the option shown as $67,227.50 (interpreting the given as $67,227.50). Small rounding differences can occur depending on whether the calculator uses more precise intermediate values, but this option is the one that matches the calculated total and is closest in value.

Summary of why the other options are incorrect: A and B propose totals well above what the actual accumulated values produce, given the 5% rate and timing of cash flows. C yields a total that’s too low compared with the precise accumulation of the cash flows to year 5. D best matches the computed accumulation, acknowledging minor rounding differences.

What is the future value at the end of Year 5 for the following cash flow stream, assuming an interest rate of 5.0%? Beginning of Year 1 = $5,000 Beginning of Year 2 = $20,000 End of Year 3 = $15,000 End of Year 5 = $20,000单项选择题

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