The information in the table shows
how much a specific monthly
contribution can result in after 3
years of investment with a 4.2%
annual interest rate, compounded
monthly.
On average, the annual cost to
attend a 2-year public institution in
the 2020-2021 academic year is
$3,900. If the goal is to cover the
cost for two years at a 2-year public
institution after 3 years of
investment, what is the minimum
amount a student should be saving
each month?
Based on the provided table, the total amount after 3 years of investment with a 4.2% annual interest rate, compounded monthly, for different monthly contributions is as follows:
Monthly Contribution (dollars) | Total Amount After 3 Years of Investment (dollars)
------------------------------------------------------------------------------------------------------------------
125 | 4,803.64
175 | 6,725.09
225 | 8,646.54
300 | 11,528.72
To find the minimum amount a student should be saving each month to cover the cost for two years at a 2-year public institution after 3 years of investment, we need to consider the total amount after 3 years and find the lowest contribution amount that is equal to or greater than the cost of two years at a 2-year public institution ($3,900).
Looking at the table, we can see that a monthly contribution of $225 results in a total amount after 3 years of $8,646.54, which is more than enough to cover the cost of two years at a 2-year public institution ($3,900).
Therefore, the minimum amount a student should be saving each month to cover the cost for two years at a 2-year public institution after 3 years of investment is $225.
To develop a plan for Estrella to save $26,000 for a two-year program at a community college while working for two years, we need to consider her income, expenses, and savings goals.
1. Determine Estrella's income: Estrella will work for 50 weeks a year. Let's assume she earns a consistent income throughout the two years. Let's also assume she earns $X per week.
2. Determine Estrella's expenses: Estrella will be living at home, so her major expenses may include transportation, food, personal expenses, and any other necessary expenses. Let's assume her total expenses per week are $Y.
3. Calculate Estrella's savings: Estrella's savings can be calculated by subtracting her expenses from her income per week. So her weekly savings can be expressed as:
Weekly savings = Income per week - Expenses per week.
4. Calculate Estrella's total savings over two years: Multiply Estrella's weekly savings by the number of weeks she will work in two years (50 weeks per year). So her total savings over two years can be expressed as:
Total savings = Weekly savings * 50 weeks per year * 2 years.
Now, we need to solve the equation Total savings = $26,000 to find the appropriate income and expense levels.
The equation becomes:
$26,000 = Weekly savings * 50 weeks per year * 2 years.
Simplifying the equation:
Weekly savings = $26,000 / (50 weeks per year * 2 years).
Using a calculator, we find that the weekly savings required to reach $26,000 in two years is approximately $260.
To meet Estrella's savings goal, she would need to save approximately $260 per week.
Please note that this plan assumes Estrella's income, expenses, and savings remain constant throughout the two-year period. It's important for Estrella to track her expenses and adjust her savings plan accordingly to ensure she reaches her savings goal.
The table is not provided, so we do not have the exact information on how much a specific monthly contribution can result in after 3 years of investment with a 4.2% annual interest rate, compounded monthly.
However, we can calculate the minimum amount a student should be saving each month to cover the cost for two years at a 2-year public institution after 3 years of investment based on the given information.
Let's assume that the student needs to save x amount each month for 3 years to cover the cost for two years at a 2-year public institution.
Using the compound interest formula A = P(1 + r/n)^(nt), where:
A = the final amount after n years,
P = the principal amount (initial monthly contribution),
r = annual interest rate (4.2% = 0.042),
n = number of times the interest is compounded per year (12 in this case),
t = number of years (3 in this case).
The final amount after 3 years of investment can be calculated as:
A = P(1 + r/n)^(nt)
A = x(1 + 0.042/12)^(12*3)
A = x(1 + 0.0035)^(36)
A = x(1.0035)^(36)
We want this final amount to be equal to or greater than $3,900, the average annual cost to attend a 2-year public institution.
So, we need to solve the inequality:
x(1.0035)^(36) ≥ $3,900
To find the minimum monthly contribution x, we divide both sides of the inequality by (1.0035)^(36):
x ≥ $3,900 / (1.0035)^(36)
Using a calculator, we can compute the right-hand side of the inequality:
x ≥ $3,900 / 1.151
Therefore, the minimum amount a student should be saving each month to cover the cost for two years at a 2-year public institution after 3 years of investment is at least $3,384.82 (rounded to the nearest cent).
Monthly
Contribution
(dollars)
125
175
225
300
Total Amount
After 3 Years of
Investment
with a 4.2%
Annual Interest
Rate (dollars)
4,803.64
6,725.09
8,646.54
11,528.72
After graduating from high school,
Estrella plans to work for two years
while living at home. She will work
50 weeks a year. Develop a plan
that will enable her to save $26,000
for a two-year program at a
community college. (1 point)
Arianna has just had a child. She
and her husband's net income is
$60,000 a year between them. She
has established a savings account
for her child that needs to contain
$90,000 after 18 years. What
percent of her household's income
will need to be set aside for the
baby's college fund? (1 point)
To determine what percent of Arianna and her husband's household income needs to be set aside for the baby's college fund, we can follow these steps:
1. Calculate the total household income over 18 years: Given that their net income is $60,000 per year, their total household income over 18 years can be calculated as:
Total household income = Net income per year * Number of years
Total household income = $60,000 * 18
Total household income = $1,080,000
2. Determine the amount needed for the baby's college fund: Arianna wants the savings account for her child to contain $90,000 after 18 years.
3. Calculate the percentage of the household income that needs to be set aside for the baby's college fund: Divide the amount needed for the college fund by the total household income and then multiply by 100 to get the percentage.
Percentage = (Amount needed / Total household income) * 100
Percentage = ($90,000 / $1,080,000) * 100
Using a calculator, we can compute the value of the percentage:
Percentage ≈ 8.33%
Therefore, Arianna and her husband will need to set aside approximately 8.33% of their household income for the baby's college fund.
Eben figures he can work a part-
time job for 20 hours a week, 50
weeks a year, for the next four years
to earn money for his higher
education. He wants to pursue a
two-year program at a community
college and figures he will need
$22,500 each year for tuition, fees,
and living expenses. What is the
minimum he must make per hour?
To determine the minimum hourly wage that Eben must make to cover his expenses for a two-year program at a community college, we need to consider his annual expenses and the number of hours he plans to work.
1. Calculate Eben's annual expenses: Eben estimates that he will need $22,500 each year for tuition, fees, and living expenses during his two-year program.
2. Determine the total amount of money Eben needs to earn over the four years: Multiply Eben's annual expenses by the number of years.
Total expenses = Annual expenses * Number of years
Total expenses = $22,500 * 2
Total expenses = $45,000
3. Calculate the total number of hours Eben will work over the four years: Multiply the number of hours per week by the number of weeks per year and by the number of years.
Total hours worked = Hours per week * Weeks per year * Number of years
Total hours worked = 20 hours/week * 50 weeks/year * 4 years
Total hours worked = 4,000 hours
4. Calculate the minimum hourly wage that Eben must make to cover his expenses: Divide the total expenses by the total number of hours worked.
Minimum hourly wage = Total expenses / Total hours worked
Minimum hourly wage = $45,000 / 4,000 hours
Using a calculator, we can compute the value of the minimum hourly wage:
Minimum hourly wage = $11.25
Therefore, the minimum hourly wage that Eben must make to cover his expenses for a two-year program at a community college is $11.25.