Charlie wants to take out a car title loan for $8000.The interest rate is 32.19% per year and the loan term is 4 years.Use the ALEKS loan calculator for the following.Also use the regular ALEKS calculator, as necessary.Write your answers to the nearest cent.ALEKS Loan CalculatorLoan amount:$ Loan term: yearsInterest rate: %Monthly payment:Calculate(a) Find the monthly payment.$(b) Find the total amount to repay the loan.$(c) Find the total amount of interest that will be paid.$
Question
Charlie wants to take out a car title loan for Loan term: yearsInterest rate: %Monthly payment:Calculate(a) Find the monthly payment.(c) Find the total amount of interest that will be paid.$
Solution
To solve this problem, we will use the formula for calculating the monthly payment for a 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)
(a) Find the monthly payment.
First, we need to convert the annual interest rate to a monthly rate by dividing by 12:
r = 32.19% / 12 = 2.6825%
Next, we convert this percentage to a decimal by dividing by 100:
r = 2.6825 / 100 = 0.026825
Now we can plug the values into the formula:
P = [0.026825 * 263.65
So, the monthly payment is approximately $263.65.
(b) Find the total amount to repay the loan.
The total amount to repay the loan is simply the monthly payment times the number of payments:
Total repayment = P * n = 12,655.20
So, the total amount to repay the loan is approximately $12,655.20.
(c) Find the total amount of interest that will be paid.
The total amount of interest paid is the total repayment minus the original loan amount:
Total interest = Total repayment - PV = 8000 = $4,655.20
So, the total amount of interest that will be paid is approximately $4,655.20.
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