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.(1 point)
The formula to calculate the total amount to be paid back on a loan with compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan (total amount to be paid back)
P = the principal amount (initial amount borrowed)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $25,000
r = 0.05 (5% expressed as a decimal)
n = 1 (compounded annually)
t = 4
A = 25000(1 + 0.05/1)^(1*4)
A = 25000(1 + 0.05)^4
A = 25000(1.05)^4
Using a calculator, we find that (1.05)^4 is approximately 1.21550625.
A = 25000(1.21550625)
A ≈ $30,387.66
Therefore, Jonathan will need to pay back approximately $30,387.66 when he finishes college.