To calculate how much Sarah Wiggum needs to invest today (Present Value) to have $1.7 million at retirement in 30 years, we use the formula for Present Value (PV) in compound interest:

$PV = \dfrac{FV}{(1 + r)^n}$

Where:

• $FV$ is the future value, which is $1,700,000.
• $r$ is the annual interest rate (8% or 0.08).
• $n$ is the number of years (30 years).

Now, let's calculate:

$PV = \dfrac{1,700,000}{(1 + 0.08)^{30}}$

$PV = \dfrac{1,700,000}{(1.08)^{30}}$

I will calculate this next.The amount Sarah Wiggum needs to invest today is approximately $168,941.47 to reach $1.7 million in 30 years at an 8% annual return.

Would you like me to calculate how soon she could retire with a 17% annual return? Let me know if you have any questions.

Here are 5 related questions to explore:

1. What would happen if Sarah could only invest for 20 years instead of 30?
2. How would different interest rates impact the required initial investment?
3. What if Sarah wanted $2 million instead of $1.7 million?
4. How does compound interest differ from simple interest in these calculations?
5. What if Sarah could make monthly investments instead of a single one?

Tip: Small changes in the interest rate have a large effect on long-term investments due to compounding.