To help open up a wine bar, Deshaun borrowed money from an online lending company.He took out a personal, amortized loan for $44,500, at an interest rate of 6.7%, with monthly payments for a term of 6 years.For each part, do not round any intermediate computations and round your final answers to the nearest cent.If necessary, refer to the list of financial formulas.(a) Find Deshaun's monthly payment.$(b) If Deshaun pays the monthly payment each month for the full term, find his total amount to repay the loan.$(c) If Deshaun pays the monthly payment each month for the full term, find the total amount of interest he will pay.
Question
To help open up a wine bar, Deshaun borrowed money from an online lending company.He took out a personal, amortized loan for (b) If Deshaun pays the monthly payment each month for the full term, find his total amount to repay the loan.$(c) If Deshaun pays the monthly payment each month for the full term, find the total amount of interest he will pay.
Solution
(a) To find Deshaun'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 = monthly payment r = monthly interest rate (annual rate / 12) PV = present value, i.e., the amount of the loan n = number of payments (months)
First, we need to convert the annual interest rate to a monthly rate: 6.7% / 12 = 0.00558333 (or 0.0056 approx).
Then we can substitute the values into the formula:
P = [0.0056 * 44500] / [1 - (1 + 0.0056)^-72]
P = [249.2] / [1 - 0.3274]
P = $249.2 / 0.6726
P = $370.70
So, Deshaun's monthly payment is approximately $370.70.
(b) To find the total amount to repay the loan, we multiply the monthly payment by the number of payments:
Total repayment = P * n
Total repayment = $370.70 * 72
Total repayment = $26,690.40
So, if Deshaun pays the monthly payment each month for the full term, he will repay a total of approximately $26,690.40.
(c) To find the total amount of interest paid, we subtract the original loan amount from the total repayment:
Total interest = Total repayment - PV
Total interest = 44,500
Total interest = -$17,809.60
So, if Deshaun pays the monthly payment each month for the full term, he will pay approximately $17,809.60 in interest.
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