Middle School

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20. Ferris purchased a car for $16,720. He made a down payment of $1,940. He applied for a five-year installment loan with an interest rate of 8.1%.

What is the total cost of the car after five years?

Answer :

Answer: $21817.4 I am not sure.

Explanation: I think it needs to add the down payment portion too.

$21817.4+$1940=$23757.4

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Rewritten by : Barada

The total cost comes to approximately $20,115.80, including all interest and principal payments.

First, calculate the loan amount:

Loan Amount = Car Price - Down Payment = $16,720 - $1,940 = $14,780

Next, use the formula for calculating monthly payments on an installment loan:

Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

  • P is the loan principal: $14,780
  • r is the monthly interest rate: 8.1% annual rate / 12 months = 0.675% per month = 0.00675
  • n is the total number of payments: 5 years * 12 months = 60

Calculate:

Monthly Payment = ($14,780 × 0.00675 × [tex]((1 + 0.00675)^{60})[/tex] / ((1 + 0.00675)^60 - 1) ≈ $302.93

Total cost of the loan over 5 years:

Total Loan Cost = Monthly Payment × n = $302.93 × 60 = $18,175.80

Finally, add the down payment to get the total cost of the car:

Total Cost = Total Loan Cost + Down Payment = $18,175.80 + $1,940 = $20,115.80

So, the total cost of the car after five years is approximately $20,115.80.