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Part 1

**Present value**   For the case shown in the following​ table, calculate the present value of the cash​ flow, discounting at the rate given and assuming that the cash flow is received at the end of the period noted.  ​(Click on the icon here 

    

in order to copy the contents of the data table below into a​ spreadsheet.)

**Single cash flow**

**Discount rate**

**End of period**​ (years)

​$132 comma 000132,000

1919​%

1111

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Part 1

The present value is 

​$19,478.5819,478.58.

  ​(Round to the nearest​ cent.) 132,000	19	11

To calculate the present value (PV) of a future cash flow, we use the following formula:

\[
PV = \frac{FV}{(1 + r)^t}
\]

Where:
- $FV$ is the future value (in this case, \$132,000),
- $r$ is the discount rate (19% or 0.19),
- $t$ is the time period in years (11 years).

Let's calculate the present value step by step.

### Step-by-step solution:

\[
PV = \frac{132,000}{(1 + 0.19)^{11}}
\]

Now, I'll compute this value.The present value of the cash flow is approximately **$19,478.58**, which matches the given solution when rounded to the nearest cent.

Would you like more details on the steps, or do you have any questions?

Here are five related questions:
1. How would the present value change if the discount rate were 15%?
2. What is the future value formula if the present value and rate are known?
3. How does the number of periods affect the present value of a cash flow?
4. How would the present value differ if the cash flow were received at the start of the period?
5. How does compounding frequency impact the present value of a cash flow?

**Tip:** A higher discount rate reduces the present value of future cash flows significantly over long periods.

For the case shown in the following table, calculate the present value of the cash flow, discounting at the rate given and assuming that the cash flow is received at the end of the period noted. The cash flow is $132,000, the discount rate is 19%, and the end of the period is 11 years. The present value is $19,478.58.

Learn how to calculate the present value of a $132,000 cash flow, discounted at 19% over 11 years. This problem involves the concept of present value in finance and demonstrates how to apply the formula PV = FV / (1 + r)^t for long-term cash flows.

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