Assume that your parents wanted to have 

​$120 comma 000120,000 

saved for college by your 

1818th 

birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 

9 %9% 

per year on their investments. 

**a.** How much would they have to save each year to reach their​ goal? 

**b.** If they think you will take five years instead of four to graduate and decide to have 

​$150 comma 000150,000 

saved just in​ case, how much would they have to save each year to reach their new​ goal? 

Question content area bottom

Part 1

**a.** How much would they have to save each year to reach their​ goal? 

To reach the goal of 

​$120 comma 000120,000​, 

the amount your parents have to save each year is 

​$2,905.472,905.47. 

 ​(Round to the nearest​ cent.)

Part 2

**b.** If they think you will take five years instead of four to graduate and decide to have 

​$150 comma 000150,000 

saved just in​ case, how much would they have to save each year to reach their new​ goal? 

To reach the goal of 

​$150 comma 000150,000​, 

the amount your parents have to save each year is 

​$enter your response here. 

** ​(Round to the nearest​ cent.

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!

Assume that your parents wanted to have $120,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 9% per year on their investments.

Part 1: How much would they have to save each year to reach their goal?

Part 2: If they think you will take five years instead of four to graduate and decide to have $150,000 saved just in case, how much would they have to save each year to reach their new goal?

Learn how to calculate the annual savings required to reach a college fund goal of $120,000 by the age of 18, with a 9% interest rate. Understand how compound interest impacts the future value of an annuity and see how adjusting the savings goal to $150,000 affects the yearly savings needed. Suitable for Grades 11-12.

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