Final answer:
Juan's monthly payment is $647.04. If he pays the monthly payment each month for the full term of 8 years, he will repay a total of $62,162.57. The total amount of interest he will pay is $15,162.57.
Step-by-step explanation:
To find Juan's monthly payment for the loan, we can use the formula for the monthly payment of an amortized loan:
Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
- P is the principal amount of the loan ($47,000)
- r is the monthly interest rate (6.15%/12 = 0.05125)
- n is the total number of monthly payments (8 years * 12 months = 96)
Plugging in the values, we have:
Monthly payment = 47000 * 0.05125 * (1 + 0.05125)^96 / ((1 + 0.05125)^96 - 1)
Using a calculator, the monthly payment comes out to be approximately $647.04. Therefore, Juan's monthly payment is $647.04.
To find the total amount to repay the loan, we multiply the monthly payment by the total number of payments:
Total amount to repay the loan = Monthly payment * Number of payments = $647.04 * 96 = $62,162.57
Therefore, if Juan pays the monthly payment each month for the full term, the total amount to repay the loan is $62,162.57.
To find the total amount of interest Juan will pay, we subtract the principal amount of the loan from the total amount to repay the loan:
Total amount of interest = Total amount to repay the loan - Principal amount of the loan = $62,162.57 - $47,000 = $15,162.57
Therefore, if Juan pays the monthly payment each month for the full term, the total amount of interest he will pay is $15,162.57.