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.

Answer 1

The computation of the downpayment Reg's purchase has been given below, kindly go through them closely.

Option d is the down payment from the given choices for the Reg's situation.

Given

There was a 7.96 percent sales tax, a $2,138 car registration fee, and a $262 documentation fee included in the price.

$\text{Total Amount} = 7.69$ % × $22,499 + 262 + 2,138 + 2,249 =$ $ $26,689.92$

Reg's loan has a three-year term and an interest rate of 10.27 percent, compounded monthly.

$r = 10.27$%
$n=12\text{ x } 3\\\ n=36$

Reg makes a monthly payment of $773.89 as well.

Step-by-step Computation

$\text{ Monthly payment} = 773.89\\\\\\773.89= \frac{(22,499 - x) \text{ x } \frac{10.27}{1,200}} {1-(1+\frac{10.27}{1,200} }$

$x = 23889.84 \text{ dollars}$

$\text{ Down payment = Total Amount - 23,889.84}$

$\text{ Down payment = 26,689.92 - 23,889.84}$

$\text{ Down payment} = 2,800.08 \\\text{i.e} = 2,800 \text{ dollars}$

For more information about the down payment, refer below

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