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To help open up a wine bar, Diane borrowed money from her credit union.She took out a personal, amortized loan for $42,500, at an interest rate of 6.55%, with monthly payments for a term of 7 years.For each part, do not round any intermediate computations and round your final answers to the nearest cent.If necessary, refer to the list of financial formulas.(a) Find Diane's monthly payment.$(b) If Diane pays the monthly payment each month for the full term, find her total amount to repay the loan.$(c) If Diane pays the monthly payment each month for the full term, find the total amount of interest she will pay.

Question

To help open up a wine bar, Diane borrowed money from her credit union.She took out a personal, amortized loan for 42,500,ataninterestrateof6.5542,500, at an interest rate of 6.55%, with monthly payments for a term of 7 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 Diane's monthly payment.(b) If Diane pays the monthly payment each month for the full term, find her total amount to repay the loan.$(c) If Diane pays the monthly payment each month for the full term, find the total amount of interest she will pay.

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Solution

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

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

where: P is the monthly payment r is the monthly interest rate (annual rate / 12) PV is the present value or amount of the loan n is the number of payments (years * 12)

First, convert the annual interest rate to a monthly rate by dividing by 12:

r = 6.55% / 12 = 0.00545833

Then, calculate the number of payments:

n = 7 years * 12 = 84 payments

Now, we can calculate the monthly payment:

P = [0.00545833 * 42,500]/[1−(1+0.00545833)−84]=42,500] / [1 - (1 + 0.00545833)^-84] = 632.24

(b) To find the total amount to repay the loan, multiply the monthly payment by the number of payments:

Total repayment = P * n = 632.24∗84=632.24 * 84 = 53,108.16

(c) To find the total amount of interest paid, subtract the original loan amount from the total repayment:

Total interest = Total repayment - PV = 53,108.16−53,108.16 - 42,500 = $10,608.16

So, Diane's monthly payment is 632.24,thetotalamounttorepaytheloanis632.24, the total amount to repay the loan is 53,108.16, and the total amount of interest she will pay is $10,608.16.

This problem has been solved

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