You need to borrow $20,000 to buy a car. You can only afford to make monthly payments of $200. The bank offers 3 choices: 3-year loan at 5%, 4-year loan at 6%, and a 5-year loan at 7%.
a) What’s the monthly payment for each loan?
b) Which loan is best for your situation?
c) What’s the total amount you would pay over the term of each loan?
I will assume that the rates are per annum compounded monthly
Choice #1:
i = .05/12 , n = 36
P(1 - 1.0041666..^-36)/.0041666..=20000
P = 599.42 ---- can't afford that
Choice #2
i = .06/12 , n = 48
P(1 - 1.005^-48)/.005 = 20000
P = 469.70 ---- still can't afford it
choice #3
i = .07/12 = .0058333... , n = 60
P(1 - 1.0058333..^-60)/.0058333 = 20000
P = 396.02
Well , it looks like you can't afford that car.
To answer these questions, we need to calculate the monthly payment and the total amount paid over the term for each loan option.
a) To calculate the monthly payment, we can use the formula for the monthly payment on a fixed-rate loan:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate) ^ (-Number of months))
Let's calculate the monthly payment for each loan option:
For the 3-year loan at 5%:
Loan amount = $20,000
Monthly interest rate = 5% / 12 = 0.4167%
Number of months = 3 years * 12 months/year = 36
Using the formula, the calculation becomes:
Monthly payment = (20000 * 0.4167/100) / (1 - (1 + 0.4167/100) ^ (-36))
For the 4-year loan at 6%:
Loan amount and monthly interest rate remain the same, but the number of months is 4 years * 12 months/year = 48.
Monthly payment = (20000 * 0.5/100) / (1 - (1 + 0.5/100) ^ (-48))
For the 5-year loan at 7%:
Loan amount and monthly interest rate remain the same, but the number of months is 5 years * 12 months/year = 60.
Monthly payment = (20000 * 0.5833/100) / (1 - (1 + 0.5833/100) ^ (-60))
b) To determine which loan is best for your situation, compare the monthly payments. Ideally, you would want to choose the loan with the lowest monthly payment that you can afford.
c) To calculate the total amount paid over the term of each loan, simply multiply the monthly payment by the number of months.
Let's calculate the total amount paid over the term for each loan option:
Total amount paid = Monthly payment * Number of months
Now that we have the formulas and understanding of the process, I will calculate each value using the provided information.