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.
The formula for compound interest is A = P(1 + r/n)^(nt), where:
A is the future value of the investment/loan, including interest
P is the principal investment amount (the initial loan amount)
r is the annual interest rate (decimal)
n is the number of times that interest is compounded per year
t is the number of years the money is invested/borrowed for.
In this case, P is $25,000, r is 5% or 0.05, n is 1 (compounded yearly), and t is 4.
Plugging the values into the formula, we get:
A = 25000(1 + 0.05/1)^(1*4)
A = 25000(1 + 0.05)^4
A = 25000(1.05)^4
A = 25000(1.21550625)
A ≈ $30387.66
Therefore, Jonathan will need to pay back approximately $30,387.66 when he finishes college.