Christian has been saving up $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 calculate whether Christian's savings would be enough to cover the cost of 2 years at a 2-year public institution, we need to find the total cost for 2 years.
2 years at a 2-year public institution cost $3,900 per year, so the total cost for 2 years would be:
2 years * $3,900/year = $7,800
Now, let's calculate how long it would take Christian to reach $8,816.47 without gaining any interest.
The total amount he needs to reach is $8,816.47. Since he saves $170 per month, the number of months it would take is:
$8,816.47 / $170/month = 51.86 months
Therefore, without gaining any interest, it would take approximately 52 months (rounded up) or 4 years and 4 months for Christian to reach $8,816.47.
Comparing this to the calculated total amount Christian would have after 4 years of saving, which is $8,816.47, we can see that his savings would be enough to cover the cost of 2 years at a 2-year public institution ($7,800).