1 A college student in her senior year is considering purcha

1. A college student in her senior year is considering purchasing a new car. The price of the car is $18,500, the sales tax is 8%, and the title, license, and registration fee is $450. The dealer offered to finance 90% of the price of the car for 48 months at a nominal interest rate of 9% per year, compounded monthly.

(a) How much cash does the student need to pay at the time she purchases the vehicle?

(b) How much is the monthly payment?

Solution

(a) Price of the car = $18,500

Sales tax = 8% or 0.08

Amount of sales tax = $18,500 * 0.08 = $1,480

Title, license, and registration fee = $450

Total cost of the car = Price of the car + Sales tax + Title, license, and registration fee

                             = $18,500 + $1,480 + $450

                             = $20,430

The dealer has agreed to finance 90% of the price of the car.

The price of car = $18,500

Amount financed = 0.90 * $18,500 = $16,650

Calculate cash student need to pay at the time she purchase the car -

Cash need to pay = Total cost of the car - Amount financed = $20,430 - $16,650 = $3,780

The cash student need to pay at the time she purchase the car is $3,780.

(b) Amount financed = $16,500

This amount has been financed for 48 months at the rate of 9% per year, compounded monthly.

Time = 48 months

Rate of interest = 9/12 = 0.75% or 0.0075

Total amount to be paid = $16,500 * (1+0.0075)⁴⁸

                                   = $16,500 * 1.43

                                   = $23,595

Calculate monthly payment -

Monthly payment = Total amount to be paid/ Total number of months

                          = $23,595/48

                          = $491.56

The monthly payment is $491.56.