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?

1 answer

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.