 You are considering investing in a security that will pay you ​$5 comma 000 in 34 years.
a.  If the appropriate discount rate is 12 percent​, what is the present value of this​ investment?
b.  Assume these investments sell for ​$1 comma 759 in return for which you receive ​$5 comma 000 in 34 years.  What is the rate of return investors earn on this investment if they buy it for ​$1 comma 759​?
Question content area bottom
Part 1
a.  If the appropriate discount rate is 12 ​percent, the present value of this investment is ​$
  
106.06.  ​(Round to the nearest​ cent.)
Part 2
b.  The rate of return investors can earn on this investment if they buy it for ​$1 comma 759 is 
  
enter your response here​%.  ​(Round to two decimal​ places.)

Let's solve each part step by step.

### Part 1: Finding the Present Value (PV)

We can use the **Present Value formula** to calculate the value of the investment today if the appropriate discount rate is 12%. The formula is:

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

Where:
- $ FV $ is the future value, which is $5,000.
- $ r $ is the discount rate, which is 12% or 0.12.
- $ t $ is the time period, which is 34 years.

Substituting the given values:

\[
PV = \dfrac{5000}{(1 + 0.12)^{34}}
\]

I'll calculate this now.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still solve this with the formula I provided.

Here’s how to manually calculate:

1. Plug the values into the formula:
   \[
   PV = \dfrac{5000}{(1 + 0.12)^{34}}
   \]
   
2. First, calculate $ (1 + 0.12)^{34} $, which is the growth factor.

3. Then divide $5,000 by that result to get the present value.

For Part 2, we will need to calculate the **rate of return** using the following formula:
\[
FV = PV \times (1 + r)^t
\]
We will rearrange it to find $ r $ (rate of return).

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Do you want me to guide you through the steps for these calculations manually?

Here are some related questions to further explore this concept:
1. How does changing the discount rate affect the present value of an investment?
2. What is the formula for calculating compound interest and how is it applied in investments?
3. Why do investors use present value when evaluating long-term investments?
4. What happens to the present value if the time period is reduced but the future value and discount rate remain constant?
5. How do taxes affect the calculation of future investment returns?

**Tip**: Always ensure you're clear on the units and context (such as percentages or time periods) when using financial formulas.

You are considering investing in a security that will pay you $5,000 in 34 years.
 a. If the appropriate discount rate is 12 percent, what is the present value of this investment?
 b. Assume these investments sell for $1,759 in return for which you receive $5,000 in 34 years. What is the rate of return investors earn on this investment if they buy it for $1,759?

Learn how to calculate the present value of a $5,000 investment due in 34 years with a 12% discount rate. Also, determine the rate of return when investing $1,759 for the same future payout. This guide includes key financial concepts like the time value of money and the formulas used to compute present value and rate of return.

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