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 calculate the total amount Christian would have after 4 years with a monthly contribution of $170 and a 3.75% annual interest rate compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (monthly contribution)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, P = $170, r = 0.0375, n = 12, and t = 4.
A = 170(1 + 0.0375/12)^(12*4)
A ≈ 170(1 + 0.003125)^(48)
A ≈ 170(1.003125)^(48)
A ≈ 170(1.170951142)
A ≈ $8,816.47
So, Christian would have a total of $8,816.47 after 4 years of saving with the given interest rate.
The annual cost of a 2-year public institution is $3,900. Therefore, 2 years of education would cost $3,900 * 2 = $7,800.
Since $8,816.47 is greater than $7,800, this amount would be enough to cover the cost of 2 years at a 2-year public institution.
If Christian were to save the money without gaining any interest, to calculate approximately how long it would take him to reach $8,816.47, we can divide the total amount by the monthly contribution:
Time = Total Amount / Monthly Contribution
Time = $8,816.47 / $170
Time ≈ 51.86 months
So, it would take Christian approximately 52 months to reach $8,816.47 if he saved the money without gaining any interest.