Giselle used the table to predict the cost of one year of college.
Giselle predicts that she will receive a grant for [tex]$4,000[/tex]. If she has 4 years in which to save, what is the minimum monthly amount she should deposit in an interest bearing savings account to be able to pay her contribution for one year of college?
A. [tex]$400[/tex]
B. [tex]$500[/tex]
C. [tex]$600[/tex]
D. [tex]$700[/tex]
Answer (2)
To save for her college contribution, Giselle needs to accumulate $24,675 after accounting for her $4,000 grant. Saving over 48 months means she needs approximately $514 per month. The closest option available is $600, which is the best choice for her minimum monthly deposit.
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Calculate the total cost of one year of college: $12 , 450 + $10 , 125 + $2 , 600 + $2 , 250 + $1 , 250 = $28 , 675 .
Subtract the grant from the total cost: $28 , 675 − $4 , 000 = $24 , 675 .
Calculate the number of months to save: 4 × 12 = 48 months.
Divide the amount to save by the number of months: 48 $24 , 675 = $514.0625 . Round up to the next option: $600 .
Explanation
Calculate the Total Cost First, we need to calculate the total cost of one year of college. We add up all the individual costs: tuition, room and board, transportation, books and fees, and other expenses.
Sum the Costs The total cost is:
Total Cost = tuition + room and board + transportation + books and fees + other
Total Cost = $12 , 450 + $10 , 125 + $2 , 600 + $2 , 250 + $1 , 250 = $28 , 675
Calculate the Amount to Save Next, we subtract the grant amount from the total cost to find out how much Giselle needs to save.
Subtract the Grant The amount to save is:
Amount to Save = Total Cost − Grant
Amount to Save = $28 , 675 − $4 , 000 = $24 , 675
Calculate the Number of Months Now, we calculate the number of months Giselle has to save. Since she has 4 years, and there are 12 months in a year:
Multiply Years by Months per Year The number of months is:
Number of Months = 4 years × 12 year months = 48 months
Calculate the Minimum Monthly Deposit To find the minimum monthly deposit, we divide the amount to save by the number of months.
Divide Amount to Save by Number of Months The minimum monthly deposit is:
Monthly Deposit = Number of Months Amount to Save
Monthly Deposit = 48 $24 , 675 = $514.0625
Round Up to the Nearest Dollar Since we need to find the minimum monthly amount she should deposit to be able to pay her contribution, we should round up to the nearest cent. In this case, since the answer choices are in whole dollar amounts, we should round up to the nearest dollar. Therefore, Giselle should deposit at least $515 per month. However, since this is not one of the answer choices, we should choose the next largest answer choice, which is $600.
Choose the Correct Answer Therefore, the minimum monthly amount Giselle should deposit is approximately $514.06 . Since the question asks for the minimum amount she should deposit to be able to pay her contribution, and the answer choices are in increments of 100 , w e n ee d t oro u n d u pt o t h e n e x t h u n d re d , w hi c hi s $600 . Ho w e v er , s in ce w e a re l oo kin g f or t h e minim u mm o n t h l y am o u n t s h es h o u l dd e p os i t , w es h o u l d ro u n d u pt o t h e n e a res t ce n t , w hi c hi s $514.07 . S in ce t hi s i s n o t an o pt i o n , w ec h oose t h e n e x tl a r g es t an s w erc h o i ce , w hi c hi s $600$.
State the Final Answer The minimum monthly amount Giselle should deposit is $514.0625 . Rounding this value to the next highest dollar amount from the options provided gives us $600 .
Examples
Saving for college is a common goal, and this problem demonstrates how to plan for it. Imagine you want to buy a car in 5 years. You estimate the car will cost $15,000, and you have no savings. If you want to save enough money to buy the car, you can calculate the monthly deposit needed. First, you determine the total amount you need to save, which is $15,000. Then, you calculate the number of months you have to save: 5 years * 12 months/year = 60 months. Finally, you divide the total amount by the number of months: $15,000 / 60 months = $250 per month. Therefore, you need to save $250 per month to buy the car in 5 years.
