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)

Answer 1

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.