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?
(1 point)
Responses
$125
$225
$175
$300
Based on the given information, we need to find the minimum monthly contribution that can result in enough to cover the cost for two years at a 2-year public institution after 3 years of investment.
Using the compound interest formula: A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the monthly contribution
r = the annual interest rate (4.2% in this case)
n = the number of times the interest is compounded per year (12, since it is compounded monthly)
t = the number of years (3 in this case)
We can plug in the given values and solve for P:
A = P(1 + r/n)^(nt)
A = 2 * $3,900 = $7,800 (to cover two years)
P(1 + 0.042/12)^(12*3) = $7,800
P(1 + 0.0035)^(36) = $7,800
P(1.0035)^(36) = $7,800
P = $7,800 / (1.0035)^(36)
P ≈ $220.60
Therefore, the minimum amount a student should be saving each month is approximately $221.
So, the correct answer is $225.