Corbin is a student who was just accepted for a $75,000 student loan that has a 3.5% annual interest rate that is compounded monthly. the loan's term is 20 years. corbin wants to know the total amount of money he will pay over the course of the loan. calculate this amount, rounding to the nearest cent.
To calculate the total amount of money Corbin will pay over the course of the loan, we need to determine the monthly payment amount and then multiply it by the total number of payments.
First, we need to calculate the monthly interest rate. We divide the annual interest rate by 12 (the number of months in a year) and convert it to a decimal: 3.5% / 12 = 0.002917.
Next, we need to calculate the total number of payments. Since the loan term is 20 years and it is compounded monthly, the total number of payments is 20 years * 12 months = 240 payments.
Now, we can use the loan formula to calculate the monthly payment amount (PMT):
PMT = (PV * i) / (1 - (1 + i)^(-n))
where PV is the loan amount, i is the monthly interest rate, and n is the total number of payments.
Given that Corbin's loan amount is $75,000, i = 0.002917, and n = 240, we can substitute these values into the formula:
PMT = (75000 * 0.002917) / (1 - (1 + 0.002917)^(-240))
PMT ≈ 426.53
The monthly payment amount is approximately $426.53.
Finally, we can calculate the total amount of money Corbin will pay over the course of the loan by multiplying the monthly payment by the total number of payments:
Total amount = PMT * n
Total amount = 426.53 * 240
Total amount ≈ $102,367.20
Therefore, Corbin will pay a total amount of approximately $102,367.20 over the course of the loan.
To calculate the total amount of money Corbin will pay over the course of the loan, we can use the formula for the future value of an ordinary annuity:
FV = P * (((1 + r)^n) - 1) / r
Where:
FV = Future value (total amount to be paid)
P = Monthly payment
r = Monthly interest rate
n = Total number of payments
First, we need to calculate the monthly interest rate (r):
r = (3.5% / 100) / 12 = 0.0029167
Next, we need to calculate the total number of payments (n):
n = 20 years * 12 months = 240 payments
Now, let's calculate the monthly payment (P):
P = Loan amount / Total number of payments
P = $75,000 / 240 = $312.50
Finally, we can calculate the total amount to be paid (FV):
FV = $312.50 * (((1 + 0.0029167)^240) - 1) / 0.0029167 ≈ $90,127.27
Therefore, Corbin will pay approximately $90,127.27 over the course of the loan.