Respuesta :
The principal balance can be obtained by total cost. The total cost would be the sum of the cost for the car and sales tax.
The principal balance at the the start of the loan is [tex]\$15,030.02[/tex].
Given:
The cost for the car is [tex]\$15,867.00[/tex].
The sales tax is [tex]5.25\%[/tex].
The down payment is [tex]10\%[/tex].
Convert the percent in to decimal.
[tex]5.25\%=\dfrac{5.25}{100}=0.0525[/tex]
Calculate the total cost of the car.
[tex]\begin{aligned} \rm{Total\: cost} &= \rm {Cost \:of\: the\: car + sales\: tax)\\&= \$ 15,867 + \$ (15,867\times 0.0525)\\&= \$ 15,867.00 + \$ 833.02\\&= \$ 16,700.02\end{aligned}[/tex]
Calculate the down payment.
[tex]\begin{aligned}\\10\% \rm{of\: the\: total\: cost} &= 0.1\times $16,700.02\\ &= $1,670.00\\\end[/tex]
The principal balance is as follows,
[tex]\begin{aligned} \rm {Principal\: balance} &= \rm {Total\: cost} - \rm {down\: payment}\\&=( \$ 16,700.02 - \$ 1,670.00)\\&= \$ 15,030.02\\\end[/tex]
Thus, the principal balance at the the start of the loan is [tex]\$15,030.02[/tex].
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