Question

Charles is going to purchase a new car that has a list price of $21,450. He is planning on trading in his good-condition 2004 Dodge Neon and financing the rest of the cost over three years, paying monthly. His finance plan has an interest rate of 12. 28%, compounded monthly. Charles will also be responsible for 6. 88% sales tax, a $1,089 vehicle registration fee, and a $124 documentation fee. If the dealer gives Charles 80% of the listed trade-in price on his car, once the financing is paid off, what percent of the total amount paid will the interest be? (Consider the trade-in to be a reduction in the amount paid. ).

Answer 1

The Interest rate is the rate that is charged by the lender for the use of his money.

The percent of the total amount paid by Charles would be the on the interest of 16.70%.

What is the interest rate?

The interest rate is the amount of interest that is due per period, as a quotient of the amount deposited, or borrowed.

The amount of interest depends upon the sum of the principal, and it can vary by the amount of money lent or deposited.

Computation of the rate of interest:

Given,

List Price = $21,450,

Interest Rate on the finance plan = 12.28%,

Monthly Interest rate:

$\dfrac{12.28\%}{12} = 1.023\%$

Sales Tax Rate = 6.88%

$n = 12 \text{Months}\times3\text{Years}\\n=36 \text{Months}$

Registration and documentation fee = $1,213 ($1,089 +$124)

Then,

The amount after-tax on selling neon 2004 is:

 

$=\ 6,591\times80\% \times ( 1 - 6.88\%) \\\\= \ 4,910$

Then the total amount paid for a new car is:

$\text{Amount Paid For a New Car}= \text{List Price+ Documentation Fee + Registration Fee}\\\\\\\text{Amount Paid For a New Car}=\ 21,450 +\ 1,089 + \ 124\\\\\\\text{Amount Paid For a New Car}= \ 22,663$

And, The total amount gets from the finance plan:

$\text{Net Amount Paid For a New Car - Amount After Tax}\\\\\\ \ 22,663 - \ 4,910 = \ 17,753$

so, Present Value = $17,753

Now, apply the given values in the formula of annuity, we get the monthly payment:

$\text{A} =\text{PV}\times {1- (1+i)^n }}\\\\\text{A} = \ 592$

Where A = Annuity

Then, The total repayment in Charles finance plan would be:

$\ 592\times36 = \ 21,312$

The total interest expenses would be:

$\text{Total repayment - Financing Amount} \\\\ \ 21,312 - \ 17,753 = \ 3,559$

Therefore, the percentage of total interest expenses in the amount paid is :

$\dfrac{3,559}{21,312}= 16.70\%$

Hence, The rate of interest would be 16.70%.

Learn more about the interest rate, refer to:

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