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.