 Given the following cash inflow at the end of each​ year, what is the future value of this cash flow at 5 %​, 8 %​, and 17​% interest rates at the end of year​ 7?                                                 
Year	Cash Inflow
1	14,000
2	22,000
3	30,000
4	0
5	0
6	0
7	130,000

To calculate the future value of the cash inflows at the end of year 7, we can use the formula for the future value (FV) of a cash flow, which is:

\[
FV = C \times (1 + r)^{(n-t)}
\]

Where:
- $ C $ is the cash inflow in a given year.
- $ r $ is the interest rate (5%, 8%, or 17% in this case).
- $ n $ is the number of years for the future value (in this case, 7).
- $ t $ is the year in which the cash inflow occurs.

We will calculate the future value for each cash inflow at 5%, 8%, and 17%, then sum them up.

### Step-by-step breakdown:

For each year, calculate the future value:

#### For Year 1 (inflow: 14,000):
\[
FV_{1} = 14,000 \times (1 + r)^{7-1} = 14,000 \times (1 + r)^6
\]

#### For Year 2 (inflow: 22,000):
\[
FV_{2} = 22,000 \times (1 + r)^{7-2} = 22,000 \times (1 + r)^5
\]

#### For Year 3 (inflow: 30,000):
\[
FV_{3} = 30,000 \times (1 + r)^{7-3} = 30,000 \times (1 + r)^4
\]

#### For Year 4, 5, and 6 (inflows: 0):
\[
FV_{4,5,6} = 0
\]

#### For Year 7 (inflow: 130,000):
\[
FV_{7} = 130,000 \times (1 + r)^{7-7} = 130,000
\]

Now, we can sum the future values for each interest rate: 5%, 8%, and 17%.

Let me calculate these values.The future values of the cash inflows at the end of year 7 are:

- At **5% interest**, the future value is **$213,304.72**.
- At **8% interest**, the future value is **$225,356.13**.
- At **17% interest**, the future value is **$270,362.77**.

Would you like more details on how these were calculated, or do you have any other questions?

Here are five related questions you might explore:
1. How would the future values change if the interest rate were compounded monthly instead of annually?
2. What is the present value of these cash inflows at each interest rate?
3. How does the future value change if the cash inflows in year 1 or 2 are delayed by one year?
4. What would be the impact of adding an additional cash inflow in year 5?
5. How would the calculation change if there was inflation impacting the value of cash inflows?

**Tip:** The future value increases significantly with higher interest rates, showing the power of compounding over time.

Given the following cash inflow at the end of each​ year, what is the future value of this cash flow at 5%, 8%, and 17% interest rates at the end of year​ 7? Year 1: 14,000, Year 2: 22,000, Year 3: 30,000, Year 4: 0, Year 5: 0, Year 6: 0, Year 7: 130,000.

Calculate the future value of cash flows at the end of each year for a 7-year period using 5%, 8%, and 17% interest rates. This problem involves compound interest and cash flow analysis, ideal for finance students. Cash inflows are: Year 1: 14,000, Year 2: 22,000, Year 3: 30,000, Year 7: 130,000.

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