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To help open up a wine bar, Joe borrowed money from a bank.He took out a personal, amortized loan for $40,000, at an interest rate of 6.4%, with monthly payments for a term of 8 years.For each part, do not round any intermediate computations and round your final answers to the nearest cent.If necessary, refer to the list of financial formulas.(a) Find Joe's monthly payment.$(b) If Joe pays the monthly payment each month for the full term, find his total amount to repay the loan.$(c) If Joe pays the monthly payment each month for the full term, find the total amount of interest he will pay.

Question

To help open up a wine bar, Joe borrowed money from a bank.He took out a personal, amortized loan for 40,000,ataninterestrateof6.440,000, at an interest rate of 6.4%, 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 Joe's monthly payment.(b) If Joe pays the monthly payment each month for the full term, find his total amount to repay the loan.$(c) If Joe pays the monthly payment each month for the full term, find the total amount of interest he will pay.

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Solution

(a) To find Joe's monthly payment, we will use the formula for the monthly payment on an amortized loan, which is:

P = [r*PV] / [1 - (1 + r)^-n]

where: P = monthly payment r = monthly interest rate (annual rate / 12) PV = present value, i.e., the amount of the loan n = total number of payments (years * 12)

First, we need to convert the annual interest rate to a monthly rate: 6.4% / 12 = 0.00533 (rounded to five decimal places).

Then, we substitute the given values into the formula:

P = [0.00533 * 40,000]/[1−(1+0.00533)−96]P=40,000] / [1 - (1 + 0.00533)^-96] P = 533.33 / [1 - 0.439] P = 533.33/0.561P=533.33 / 0.561 P = 950.67

So, Joe's monthly payment is approximately $950.67.

(b) To find the total amount Joe will repay over the term of the loan, we multiply the monthly payment by the total number of payments:

Total repayment = monthly payment * number of payments Total repayment = 950.67∗96Totalrepayment=950.67 * 96 Total repayment = 91,264.32

So, Joe will repay a total of approximately $91,264.32 over the term of the loan.

(c) To find the total amount of interest Joe will pay, we subtract the original loan amount from the total repayment:

Total interest = total repayment - original loan amount Total interest = 91,264.32−91,264.32 - 40,000 Total interest = $51,264.32

So, Joe will pay approximately $51,264.32 in interest over the term of the loan.

This problem has been solved

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