Assuming an interest rate of 6.9 percent, what is the value of the following cash flows four years from today?

Year	Cash Flow
1	$ 3,375
2	4,340
3	6,260
4	8,425
Multiple Choice

$23,231.48

$26,235.05

$24,780.79

$24,199.46

$25,507.92

To calculate the value of these cash flows four years from today, we need to find the **future value** of each individual cash flow. Since the interest rate is 6.9%, we will use the future value formula:

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

Where:
- $FV$ is the future value,
- $PV$ is the present value (cash flow),
- $r$ is the interest rate (6.9% or 0.069),
- $n$ is the number of years into the future we need to calculate for each cash flow.

We calculate the future value of each cash flow separately for its respective year, considering how far into the future each payment will compound.

Let's compute this.

### Step-by-step process:
1. **Year 1 Cash Flow (3 years from year 4):**
   \[
   FV_1 = 3,375 \times (1 + 0.069)^3
   \]
   
2. **Year 2 Cash Flow (2 years from year 4):**
   \[
   FV_2 = 4,340 \times (1 + 0.069)^2
   \]

3. **Year 3 Cash Flow (1 year from year 4):**
   \[
   FV_3 = 6,260 \times (1 + 0.069)^1
   \]

4. **Year 4 Cash Flow (no compounding needed, it's in year 4):**
   \[
   FV_4 = 8,425
   \]

The total future value at the end of year 4 is the sum of these future values.

Let me calculate that.The total future value of the given cash flows four years from today is **$24,199.46**.

Thus, the correct answer from the options is:

**$24,199.46**

Would you like further details on how the calculations were made, or do you have any other questions?

Here are 5 related questions to expand on this topic:
1. How would the future value change if the interest rate was increased to 8%?
2. What is the present value of these cash flows if the discount rate is 6.9%?
3. How does compounding frequency affect the future value of cash flows?
4. How would you calculate the future value if the cash flows occurred at mid-year instead of year-end?
5. What would be the future value of these cash flows after 5 years with a 6.9% interest rate?

**Tip**: When calculating future value, remember that the timing of the cash flow (how far it is from the evaluation point) significantly impacts its compounded value.

Assuming an interest rate of 6.9 percent, what is the value of the following cash flows four years from today?

Year	Cash Flow
1	$ 3,375
2	$ 4,340
3	$ 6,260
4	$ 8,425

Multiple Choice Options:
$23,231.48
$26,235.05
$24,780.79
$24,199.46
$25,507.92

Learn how to calculate the future value of cash flows assuming a 6.9% interest rate, with detailed steps. Explore concepts of interest rate compounding and the time value of money, applied to a four-year cash flow series.

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