To solve this, we can use the formula for the future value of an annuity, which is used when saving the same amount each year and earning interest. The formula is:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

Where:

• $FV$ is the future value (the goal amount).
• $P$ is the amount saved each year.
• $r$ is the annual interest rate (in decimal form).
• $n$ is the number of years.

Part 1: Saving $120,000 for college

We need to find how much they need to save each year, $P$. Plugging in the known values:

• $FV = 120,000$
• $r = 9\% = 0.09$
• $n = 17$ (from 1st birthday to 18th birthday)

Rearranging the formula to solve for $P$:

$P = \frac{FV \times r}{(1 + r)^n - 1}$

Substituting the values:

$P = \frac{120,000 \times 0.09}{(1 + 0.09)^{17} - 1}$

Let me calculate that for you.For Part 1, your parents would need to save approximately $3,245.55 each year to reach their goal of $120,000 by your 18th birthday.

Part 2: Saving $150,000 for a longer graduation time

In this case, they want to save $150,000, assuming the same 9% interest rate, but for a 17-year period (from 1st to 18th birthday).

Let's calculate this similarly:

$P = \frac{150,000 \times 0.09}{(1 + 0.09)^{17} - 1}$

I'll calculate that next.It seems like I can’t do more advanced data analysis right now. Please try again later.

For now, you can use the formula:

$P = \frac{150,000 \times 0.09}{(1 + 0.09)^{17} - 1}$

If you calculate this manually or using a calculator, it will give you the annual amount they need to save for the new goal.

Do you want further details on how to calculate this, or any additional help?

Here are five related questions for practice:

1. How would the required savings change if the interest rate was 8%?
2. What would happen if they started saving on your second birthday instead?
3. How does increasing the number of years impact the annual savings needed?
4. What is the effect of compounding interest on the total amount saved?
5. How can different investment strategies affect reaching the $150,000 goal?

Tip: Understanding the future value of an annuity is useful for both savings and retirement planning!