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To help open up a restaurant, Juan borrowed money from an online lending company.

He took out a personal, amortized loan for $47,000 , at an interest rate of 6.15% , with monthly payments for a term of 8 years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent.
If necessary, refer to the list of financial formulas.
(a) Find Juan's monthly payment.
(b) If Juan pays the monthly payment each month for the full term, find his total amount to repay the loan.
(c) If Juan pays the monthly payment each month for the full term, find the total amount of interest he will pay

User Fosna
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1 Answer

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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.

User Steve De Caux
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