Christian has been saving $170 monthly for college. The investment account set up for him has a 3.75% annual interest rate, compounded monthly. If Christian invests $170 monthly over a 4-year period, he will have a total amount of $8,816.47. On average, the annual cost of a 2-year public institution in the 2020-2021 academic year is $3,900. Would this be enough for Christian to cover the cost of 2 years at a 2-year public institution? If Christian were to save the money without gaining any interest, approximately how long would it take him to reach $8,816.47?
To find out if Christian's savings would be enough to cover the cost of 2 years at a 2-year public institution, we need to calculate the total cost of 2 years of education.
The cost of 2 years at a 2-year public institution is $3,900 per year. So, the total cost for 2 years would be $3,900 * 2 = $7,800.
Since Christian's savings after 4 years is $8,816.47, which is higher than the cost of 2 years at a 2-year public institution, he would have enough to cover the cost.
Now, let's calculate how long it would take for Christian to reach $8,816.47 without gaining any interest.
If Christian saves $170 per month, he would be able to save $170 * 12 = $2,040 per year.
To reach $8,816.47, Christian would therefore need $8,816.47 / $2,040 = 4.32 years.
So, it would take Christian approximately 4.32 years to reach $8,816.47 without gaining any interest.