he 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? (1 point)
To calculate the minimum amount a student should be saving each month, we need to calculate the future value of the monthly contributions after 3 years.
Using the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A is the future value of the investment
P is the principal (monthly contribution)
r is the annual interest rate (4.2%)
n is the number of times the interest is compounded per year (12, since it's compounded monthly)
t is the number of years (3)
We can substitute the values and solve for A:
$3,900 = P(1 + 0.042/12)^(12*3)
Simplifying the equation:
$3,900 = P(1 + 0.0035)^(36)
Dividing both sides of the equation by (1.0035)^36:
$3,900 / (1.0035)^36 = P
Using a calculator, we find:
P ≈ $122.50
Therefore, the minimum amount a student should be saving each month is approximately $122.50.