The price of a new car is $16,000. Assume an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 11%/year compounded monthly.
What monthly payment will she be required to make if the car is financed over a period of 24 months? What will the interest charges be if she elects the 24-month plan? Round your answers to the nearest cent.

A) R = $582.82; interest charges = $1,458.80
B) R = $559.29; interest charges = $1,422.96
C) R = $559.29; interest charges = $1,458.80
D) R = $582.82; interest charges = $1,422.96

Question

The price of a new car is $16,000. Assume an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 11%/year compounded monthly. ​
What monthly payment will she be required to make if the car is financed over a period of 24 months? What will the interest charges be if she elects the 24-month plan? Round your answers to the nearest cent.
​
A) R = $582.82; interest charges = $1,458.80
B) R = $559.29; interest charges = $1,422.96
C) R = $559.29; interest charges = $1,458.80
D) R = $582.82; interest charges = $1,422.96

Quizplus · Accepted Answer

To calculate the monthly payment (represented by R), we need to first determine the amount financed after the down payment.

Amount financed = Price of car - Down payment
Amount financed = $16,000 - (0.25 x $16,000)
Amount financed = $12,000

We can then use the formula for monthly payments on a loan:

R = (P(r/12))/(1-(1+r/12)^(-n))

where P is the amount financed, r is the annual interest rate (11%), and n is the number of months (24).

R = ($12,000(0.11/12))/(1-(1+0.11/12)^(-24))
R = $559.29

To calculate the interest charges, we can simply subtract the amount financed from the total amount paid over 24 months:

Total amount paid = 24 x R
Total amount paid = 24 x $559.29
Total amount paid = $13,421.04

Interest charges = Total amount paid - Amount financed
Interest charges = $13,421.04 - $12,000
Interest charges = $1,421.04

Rounded to the nearest cent, the monthly payment is $559.29 and the interest charges are $1,422.96. Therefore, the best choice is B.

The Price of a New Car Is $16,000