To determine the minimum amount of money Emily should save each month to pay for her first year of college, let’s break it down step-by-step:
1. Calculate the total cost for the first year of college:
The total cost is the sum of all the predicted costs for different categories listed in the table. We add:
[tex]\[
36,620 \text{ (tuition)} + 12,900 \text{ (room and board)} + 2,450 \text{ (books and fees)} + 3,100 \text{ (transportation)} + 1,330 \text{ (other)}
\][/tex]
This equals:
[tex]\[
36,620 + 12,900 + 2,450 + 3,100 + 1,330 = 56,400
\][/tex]
So, the total cost for the first year of college is \[tex]$56,400.
2. Calculate the net amount needed after grants:
Emily anticipates receiving \$[/tex]6,000 in grants. Therefore, we subtract this from the total cost:
[tex]\[
56,400 - 6,000 = 50,400
\][/tex]
So, the net amount Emily needs to save is \[tex]$50,400.
3. Determine the savings timeframe and monthly savings required:
Emily has 6 years to save this amount. First, convert 6 years to months:
\[
6 \text{ years} \times 12 \text{ months/year} = 72 \text{ months}
\]
Next, divide the net amount by the total number of months to find out how much she should save each month:
\[
\frac{50,400}{72} \approx 700
\]
Thus, Emily and her family should save approximately \$[/tex]700 each month for the next 6 years to cover the first year of college expenses without including any interest earned.
Hence, the most reasonable estimate from the given options is \$700.
