To determine the monthly savings needed, let's follow a step-by-step approach:
1. Calculate the total predicted cost for the first year of college:
- Tuition: [tex]$36,620
- Room and board: $[/tex]12,900
- Books and fees: [tex]$2,450
- Transportation: $[/tex]3,100
- Other expenses: [tex]$1,330
Adding these costs together:
\[
36,620 + 12,900 + 2,450 + 3,100 + 1,330 = 56,400
\]
The total predicted cost for the first year of college is $[/tex]56,400.
2. Subtract the grant amount from the total cost:
- Grants: [tex]$6,000
Subtracting the grants from the total cost:
\[
56,400 - 6,000 = 50,400
\]
The total cost after accounting for the grants is $[/tex]50,400.
3. Determine the number of months available to save:
Emily has 6 years to save. Since there are 12 months in a year, the total number of months is:
[tex]\[
6 \times 12 = 72
\][/tex]
4. Calculate the monthly savings needed:
To find out how much Emily and her family should save each month, divide the total cost after grants by the number of months:
[tex]\[
\frac{50,400}{72} = 700
\][/tex]
Therefore, the reasonable estimate of the amount Emily and her family should save each month for the next 6 years to pay for her first year of college is $700.
