To solve this problem, we'll apply the formula for the future value of an ordinary annuity. This formula helps us determine the amount your parents need to save each year to reach their savings goal, given a fixed annual interest rate and a fixed period.

Formula for Future Value of an Ordinary Annuity

The future value $FV$ of an ordinary annuity (where payments are made at the end of each period) is given by:

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

where:

• $FV$ is the future value, which is the goal amount ($120,000 for part a, $150,000 for part b).
• $P$ is the annual payment (the amount saved each year).
• $r$ is the annual interest rate (9% or 0.09 in decimal form).
• $n$ is the number of years the money is saved (17 years, since saving starts on the 1st birthday and ends on the 18th birthday).

Solving for Annual Savings (P)

We need to rearrange the formula to solve for $P$:

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

Part (a): Calculate the Annual Savings to Reach $120,000

Let's substitute the values:

• $FV = 120,000$
• $r = 0.09$
• $n = 17$

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

Now, let's calculate the value.The amount your parents would have to save each year to reach the goal of $120,000 by your 18th birthday is $3,245.55 (rounded to the nearest cent).

Part (b): Calculate the Annual Savings to Reach $150,000

For the new goal of $150,000, we use the same formula with updated values:

• $FV = 150,000$
• $r = 0.09$
• $n = 17$

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

Let's calculate this value now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can still calculate the amount manually using the formula provided earlier:

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

Feel free to ask any other questions, and I'll be happy to help!

Related Questions:

1. What if the interest rate changes to 8%? How does that affect the annual savings required?
2. How would the amount change if the savings period was extended to 20 years instead of 17?
3. What is the total amount of interest earned by the end of 18 years with the current savings plan?
4. How would the calculations change if the savings were made at the beginning of each year?
5. What is the future value if your parents saved $3,500 each year instead?

Tip: Always double-check your formulas and inputs to ensure accurate financial planning.