LAST ATTEMPT PLEASE HELP ME!!!!!!!
WILL MARK BRAINLIEST!!!!!!!!!

A customer buys an automobile from you, the salesman. The price of the car, which includes taxes and license, amounts to $5,955.00. The customer wants to finance the car over 48 months after making a $500 down payment. You inform him that the true annual interest rate is 18%.


To the nearest penny, c = $ .

Total of payments = amount financed + c = $ .

Total of payments ÷ number of payments = monthly payment = $ .


thanks so much!

Respuesta :

Answer:

  • c = $2004.71
  • total of payments = $7459.71
  • monthly payment = $155.41

Step-by-step explanation:

It appears you have a formula for c that is ...

  c = iP(n+1)/(2y)

where i is the "true annual interest rate", P is the principal amount financed, n is the total number of payments, and y is the number of payments per year.

Since there is a $500 down payment, the amount financed will be ...

  P = $5955 -500 = $5455

The other values in the formula are n=48 and y=12, so we have ...

  c = 0.18·$5455(48+1)/(2·12)

  c = $2004.71

__

Then the total of payments is ...

  total of payments = P +c = $5455 +2004.71

  total of payments = $7459.71

__

And the monthly payment will be ...

  monthly payment = $7459.71/48

  monthly payment = $155.41

_____

Comment on the question

We are used to seeing loan questions solved by computing a monthly payment, multiplying that by the number of payments to get a total repaid, then subtracting the loan amount to get the finance charge. Here, it seems you're trying to estimate the finance charge first by using a "true annual interest rate" that appears to have no relation to the (monthly or annual) interest rates usually used in loan formulas.

In conventional terminology, this payment amount corresponds to an APR of 15.96%. The amortization formula usually used would give a monthly payment of $160.24 for a 48-month loan with an APR of 18%.