Marco decides to take out a $4,000 student loan during his first year in college. If he is charged 10% interest that is compounded annually, how much will the total loan amount equal in four years when he graduates?
4000 * 1.10^4 = ____
To calculate the total loan amount after four years, we need to consider the principal amount and the interest earned.
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A is the future value (total amount)
P is the principal amount (initial loan)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, we have:
P = $4,000
r = 10% or 0.10 (in decimal form)
n = 1 (compounded annually)
t = 4 years
Now we can plug in the values into the formula to find the total loan amount after four years:
A = 4000(1 + 0.10/1)^(1*4)
A = 4000(1 + 0.10)^4
A = 4000(1.10)^4
A = 4000 * 1.4641
A ≈ $5,856.40
Therefore, the total loan amount will be approximately $5,856.40 when Marco graduates after four years.