Exxon-Mobil's receipts and disbursements are shown below. Calculate the future worth in year 7 at an interest rate of 8% per year. Year Cash Flow, S -6,000 5,000 4,000 5,000 4 5,000 5 -1,000 7,000 7 8,000 $31,023.34 O S18,101.82 O S19,998.37 O $31,312.27

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Chapter1: Investments: Background And Issues
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### Future Worth Calculation of Cash Flow Series

Exxon-Mobil's receipts and disbursements are shown below. Calculate the future worth in year 7 at an interest rate of 8% per year.

| Year | Cash Flow ($) |
|------|---------------|
| 0    | -6,000        |
| 1    | 5,000         |
| 2    | 4,000         |
| 3    | 5,000         |
| 4    | 5,000         |
| 5    | -1,000        |
| 6    | 7,000         |
| 7    | 8,000         |

Options:
- $31,023.34
- $18,101.82
- $19,998.37
- $31,312.27

**Explanation:**
To find the future worth in year 7, one must compound each cash flow to year 7 using the given interest rate of 8% per year. The future value \( FV \) is calculated using the formula:

\[ FV = PV \times (1 + r)^{n} \]

Where:
- \( PV \) is the present value (cash flow)
- \( r \) is the interest rate per period
- \( n \) is the number of periods

Each cash flow will be compounded to year 7, and the sum of all these future values will give the future worth in year 7. 

Given cash flows are at various years:
- For year 0 (initial investment), \( n = 7 \)
- For year 1 cash flow, \( n = 6 \)
- For year 2 cash flow, \( n = 5 \)
- For year 3 cash flow, \( n = 4 \)
- For year 4 cash flow, \( n = 3 \)
- For year 5 cash flow, \( n = 2 \)
- For year 6 cash flow, \( n = 1 \)
- For year 7 cash flow, \( n = 0 \)

Using this method, each future value component will be calculated, and summed to get the final future worth.
Transcribed Image Text:### Future Worth Calculation of Cash Flow Series Exxon-Mobil's receipts and disbursements are shown below. Calculate the future worth in year 7 at an interest rate of 8% per year. | Year | Cash Flow ($) | |------|---------------| | 0 | -6,000 | | 1 | 5,000 | | 2 | 4,000 | | 3 | 5,000 | | 4 | 5,000 | | 5 | -1,000 | | 6 | 7,000 | | 7 | 8,000 | Options: - $31,023.34 - $18,101.82 - $19,998.37 - $31,312.27 **Explanation:** To find the future worth in year 7, one must compound each cash flow to year 7 using the given interest rate of 8% per year. The future value \( FV \) is calculated using the formula: \[ FV = PV \times (1 + r)^{n} \] Where: - \( PV \) is the present value (cash flow) - \( r \) is the interest rate per period - \( n \) is the number of periods Each cash flow will be compounded to year 7, and the sum of all these future values will give the future worth in year 7. Given cash flows are at various years: - For year 0 (initial investment), \( n = 7 \) - For year 1 cash flow, \( n = 6 \) - For year 2 cash flow, \( n = 5 \) - For year 3 cash flow, \( n = 4 \) - For year 4 cash flow, \( n = 3 \) - For year 5 cash flow, \( n = 2 \) - For year 6 cash flow, \( n = 1 \) - For year 7 cash flow, \( n = 0 \) Using this method, each future value component will be calculated, and summed to get the final future worth.
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