Answer: $104392.80
Explanation:
To find the total amount of interest paid through the duration of the loan, first find the monthly payment of the loan. Use the formula below to find the monthly payment, where Pmt is the monthly payment, P is the principal amount of the loan, rn is the interest rate for the compounding period (usually monthly), and nt is the number of times the loan is compounded. To calculate nt, multiply the length of the loan (in years) by the value of n.
Pmt=P×rn1−(1+rn)−nt
The amount of Corbin's student loan, P, is $75,000. Since the interest rate is compounded monthly, the interest rate offered is 3.5% per year, or 0.03512 per month. The time period is 20 years, or 240 months. Substituting the values into the formula and converting the interest rate to the monthly rate yields the following.
PmtPmt=75,000×0.035121−(1+0.03512)−240≈$434.97
Multiply the monthly payment by the number of months in the loan, 240, to determine the total cost of the loan.
$434.97×240=$104,392.80
Thus, the total amount Corbin will pay is $104,392.80.