Question

Reg has just purchased a new car. The car had a list price of $22,499, and he was responsible for 7. 96% sales tax, a $2,138 vehicle registration fee, and a $262 documentation fee. Reg’s financing has an interest rate of 10. 27%, compounded monthly, and a duration of three years. If Reg makes a monthly payment of $773. 89, which of the following was his down payment? Round all dollar values to the nearest cent. A. $2,000 b. $2,200 c. $2,500 d. $2,800 Please select the best answer from the choices provided A B C D.

Answer 1

The down payment that would be paid by reg is $2,800.

What is a down payment?

A down payment is the first partial payment for the purchase of price expensive items or services, such as a car or a house. It is usually paid off in cash or equal at the time of finalizing the transaction. A loan of some kind is then asked to finance the remainder of the payment.

Computation of a down Payment:

According to the question,

The total amount of car would be:

$\text{List Price + Sales Tax + Registration Fee + Documentation Fee}\\\\\ 22,499+\ 1,791+\ 2,138+\ 262 = \ 26,690.$

r= 10.27%,

$r=\dfrac{10.27}{12\times100}\\\\\\r= 0.00855833$ ,

t= $12\times3\text{Years}=36 \text{Months}.$

Monthly Payment = $773.89.

Let X be the amount of payment that is given in the starting.

$\text{Monthly Payment} = \dfrac{\text{(List Price - x) r }}{1-(1+r)}}\\\\\\\ 773.89 = \dfrac{(22,49-\text{x )0.0085533}}{1-(1+0.0085533)}\\\\\text{x}= 23889.84$

The amount of down payment would be:

$\text{Down Payment}=\text{Total Amount - Down Payment}\\\\\\\text{Down Payment}=\ 26,690-\ 23889.84\\\\\text{Down Payment}=\ 2,801 \text{App.}$

Hence, Option D is correct.

Learn more about the down payment, refer:

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