Questions: Jamie Lee knows how hard it is to go to school, take on debt, and try to fulfill her dreams. Her sister, Rebecca, recently had a baby girl named Alexis. Jamie Lee would like to set aside a small amount per month towards Alexis's education expenses. Jamie Lee realizes this will not cover all of the costs but, she wants to help in a small way. After researching college costs and investments, Jamie Lee has the following information: Current cost of college education: 20,000 per year (Alexis will attend college in 18 years for 4 years) Expected annual inflation: 2% Expected rate of return on investment 10%

Solution Steps

To determine the estimated annual deposit needed to achieve the education fund for Alexis, we need to follow these steps:

1. Calculate the future cost of college education: Adjust the current cost of college education for inflation over the next 18 years.
2. Calculate the total cost of college education: Multiply the future annual cost by the number of years Alexis will attend college.
3. Determine the annual savings needed: Use the future value of a series of deposits factor to find out how much needs to be saved annually to reach the total cost of college education.

To find the future cost of college education per year, we adjust the current cost for inflation over 18 years using the formula:

\[ \text{Future Cost per Year} = \text{Current Cost per Year} \times (1 + \text{Inflation Rate})^{\text{Years until College}} \]

Substituting the values:

\[ \text{Future Cost per Year} = 20000 \times (1 + 0.02)^{18} \approx 28564.92 \]

Next, we calculate the total cost of college education for 4 years:

\[ \text{Total Future Cost} = \text{Future Cost per Year} \times \text{College Duration} \]

Substituting the values:

\[ \text{Total Future Cost} = 28564.92 \times 4 \approx 114259.70 \]

To find the estimated annual deposit needed, we use the future value of a series of deposits formula rearranged to solve for the annual deposit \( P \):

\[ P = \frac{\text{Total Future Cost}}{\left(\frac{(1 + r)^{n} - 1}{r}\right)} \]

Where:

• \( n = 18 \) (years until college)
• \( r = 0.1 \) (annual return rate)

Calculating the future value factor:

\[ \text{Future Value Factor} = \frac{(1 + 0.1)^{18} - 1}{0.1} \approx 45.5992 \]

Now substituting into the formula for \( P \):

\[ P = \frac{114259.70}{45.5992} \approx 2505.74 \]

Final Answer