Question

Amy Phillips needs to borrow $20,000 to purchase a new car. She can get a 3 year loan from her bank with an interest rate of 7% (compounded monthly). Calculate Amy's monthly payment.

Also how much interest (in dollars) will Amy pay over the life of the loan?

Lastly, if Amy got a 5 year loan instead of a 3 year loan, how much interest (in dollars) would she pay over the life of the loan?

Answer using formulas - no calculator or excel. Please show work. Please also tell what formula you will be using

Answer 1

Monthly interest rate r = 7%/12 = 0.5833%

For a 3 year loan

n = 12*3 = 36 months

PV = 20000

PMT = 20000/((1-(1+0.005833)^(-36))/0.005833)

PMT = 617.54

Hence, for a 3 year loan the monthly payment is $617.54

Interest over 3 years = Number of payments*Per payment amount - Principle payment

Interest over 3 years = 36*617.54-20000 =$2231.44

For a 5 year loan

n = 12*5 = 60 months

PV = 20000

PMT = 20000/((1-(1+0.005833)^(-60))/0.005833)

PMT = 396.02

Hence, for a 5 year loan the monthly payment is $396.02

Interest over 5 years = Number of payments*Per payment amount - Principle payment

Interest over 5 years = 60*396.02-20000 =$3761.2