Jonathan took out a $25,000 student loan to go to college. The loan charges 5% interest compounded
yearly. How much will Jonathan need to pay back when he finishes college in four years? Round the
answer to two decimal places.
To find out how much Jonathan will need to pay back, we need to find the future value of the loan after four years.
The formula for future value with compound interest is:
FV = P(1 + r/n)^(nt)
Where:
FV = future value
P = principal amount (initial loan)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $25,000
r = 5% = 0.05
n = 1 (compounded yearly)
t = 4 years
FV = 25000(1 + 0.05/1)^(1*4)
FV = 25000(1 + 0.05)^4
FV = 25000(1.05)^4
Now let's calculate this:
FV ≈ 25000(1.21550625)
FV ≈ 30387.66
Jonathan will need to pay back approximately $30,387.66 when he finishes college in four years.