Question

You buy a car for $18,450. You must also pay tax and license fees of $725. You have $1,500 as a down payment. Your bank will make you a 4-year car loan for the remaining amount, at 7.2% interest, but will charge you a $75 processing fee (which will be added to your loan amount).

a.) What are your monthly payments?

b.) What is your finance charge?

c.) What is the total cost of the car, including finance charges?

d.) What is the APR?

Answer 1

a) Total cost of the car including tax,licence fee and loan processing fee= 18,450+725+75=$19,275

down payment= $1500

remaining amount=19275-1500=$17,775

interest rate=7.2%

time=4 years

let the monthly payment=x

monthly interest rate=7.2/12=0.6%

17,775= x/(1+0.0006)+..................+ x/(1+0.006)⁴⁸

=> x(monthly payment)=$427.3

b) finance charge = interest accured

total payment in 48 months=427.3*48=$20,510.4

interest accured= 20,510.4-17775=$2735.4

c)Total cost of car= downpayment + sum of monthly payment= 1500+20,510=$22,010.4

d) APR (annualized percentage rate)= (1+ monthly rate)¹²-1= 7.224%