Help with this car payment math problem please!!!?
find a used car to buy, and figure out the costs of buying this car by filling in the blanks below. You don't have enough money for a down payment, and your credit history is so new that you have to get a five-year loan with an interest rate of 10% to make the purchase.
Total interest paid:
So, we decide to purchase a 2010 Pontiac Vibe 4D Wagon, because it is equipped with a dependable Toyota manufactured engine. The car can be found on Carmax.com being sold at a store in Tucson, AZ.
The asking price for the car is $14,988 excluding sales tax.
Sales tax in AZ is 6% and in Tucson 2.1%. Therefore, the total sales tax applied will be 8.1% of $14,988 or 0.081 x $14,988, which is $1,214.03.
We then add the asking price to the sales tax to get the total cost of the car, which is $16,202.03.
We know that we’re going to be making monthly payments at an annual interest rate (APR) of 10% over five years. There are 12 months in a year, so we know that we will be making a total of 60 payments.
Here is the formula for calculating the monthly payments:
P ( r / 12 ) ------------------------- -m (1 - ( 1 + r / 12 ) )
- P = principal amount (initial investment)
- r = interest rate (as a decimal)
- m = number of monthly payments
In our example, a five year (60 month) loan of $16,202.03 at 10% interest would look like this:
16,202.03 ( 0.1 / 12 ) ------------------------- -60 (1 - ( 1 + .1 / 12 ) )
The monthly payment for this car will be: $344.25.
Finally, to see the total interest paid, you'll need to multiply the monthly payment ($344.25) by the total payments (60) and then subtract the total cost ($16,202.03).
$344.25 x 60 = $20,655 - $16,202.03 = $4,452.97.
So, you paid $4,452.97 in interest.
I hope this helped and shows you that you should always make a down payment, if you can.
Make/Model: 2010 Pontiac Vibe 4D Wagon
Asking price: $14,988
Sales tax: $1,214.03
Total cost: $16,202.03
Monthly payment: $344.25
Total interest paid: $4,452.97
Total payments: 60