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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating. How much interest is accrued after the first month? Credit New Car APR (%) Used Car APR (%) 5.40 Excellent 5.65 6.35 Good 5.95 16.30 6.90 Average 17.60 Fair 7.55 9.80 10.0 Poor​

Respuesta :

Using simple interest, it is found that $97.06 of interest is accrued after the first month.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The amount of interest after t years in is modeled by:

[tex]I(t) = Prt[/tex]

In which:

  • P is the principal.
  • r is the interest rate, as a decimal.

In this problem, first we have to find the total price of purchase of the car, which is $19,725.00 plus 4.75% sales tax, hence:

[tex](1 + 0.0475) \times 19725 = 1.0475(19725) = 20662[/tex]

Then:

  • Considering a down payment of $2,175, the principal is of P = 20662 - 2175 = 18487.
  • New car and average credit rating, hence the interest rate is of 6.30%, that is, r = 0.063.
  • We want the interest earned after one month, considering the time is measured in years, we have that [tex]t = \frac{1}{12}[/tex].

Then:

[tex]I\left(\frac{1}{12}\right) = 18487(0.063)\frac{1}{12} = 97.06[/tex]

$97.06 of interest is accrued after the first month.

You can learn more about simple interest at https://brainly.com/question/25296782

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