Question

Bernie has decided to purchase a new car with a list price of $18,575. Sales tax in bernie’s state is 7. 40%, and he will be responsible for a $795 vehicle registration fee and a $110 documentation fee. Bernie plans to trade in his existing car, a 1999 buick riviera in good condition, and finance the rest of the cost for five years at an interest rate of 12. 77%, compounded monthly. Assuming that the dealer gives bernie the listed trade-in price for his car, what will his monthly payment be? round all dollar values to the nearest cent. Buick cars in good condition model/year 1998 1999 2000 2001 2002 century $929 $1,086 $1,150 $1,488 $1,595 lesabre $2,075 $2,282 $2,690 $2,935 $3,374 regal $1,676 $1,794 $2,030 $2,214 $2,566 riviera $1,291 $1,455 $1,520 $1,814 $1,959 a. $472. 05 b. $439. 12 c. $438. 20 d. $518. 23.

Answer 1

Bernie's monthly payment for the new car, after accounting for sales tax, fees, and trade-in value and calculating the loan with a 12.77% annual interest rate compounded monthly, would be $438.20.

Step-by-step explanation:

To calculate Bernie's monthly car payment, we need to follow these steps:

1. Calculate the total cost of the car including taxes and fees.
2. Subtract the trade-in value of Bernie's current car to find the amount that will be financed.
3. Use the loan formula or an amortization calculator to find the monthly payment.

The total cost of the car with taxes and fees is calculated as follows:

List price = $18,575
Sales tax = 7.40% of list price = 0.074 * $18,575 = $1,374.55
Registration fee = $795
Documentation fee = $110
Total cost = List price + Sales tax + Registration fee + Documentation fee = $18,575 + $1,374.55 + $795 + $110 = $20,854.55.

Trade-in value for Bernie's 1999 Buick Riviera is $1,455. Subtracting this from the total cost we get:

Amount to be financed = Total cost - Trade-in value = $20,854.55 - $1,455 = $19,399.55.

Now we use the loan formula to determine the monthly payment:

M = P[r(1+r)^n]/[(1+r)^n-1]
Where:
P = principal amount ($19,399.55)
r = monthly interest rate (12.77% annual / 12 months = 1.0642% per month = 0.010642)
n = number of monthly payments (5 years * 12 months/year = 60 payments)
Substituting the values we get:
M = $19,399.55[0.010642(1+0.010642)^60] / [(1+0.010642)^60-1] = $438.20.

This matches answer choice (C). Bernie's monthly payment would be $438.20 after rounding to the nearest cent.