You have saved $$6,798$ for a down payment on a new car. The monthly payment you can afford is $$406.$ You will make payments for $48$ months $($starting $1$ month from today$).$ If the relevant interest rate is $0\mathrm{.}52\%$ per month $($this is an Effective Monthly Rate$),$ the price of the car you can afford $($taking into account the down payment as well$)$ is $$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.$

Hint: Loan problems are typically PV annuity problems, where the amount you are borrowing is the PV of the series of future payments.

Margin of error for correct responses: $+/-\mathrm{.}05$

Rounding and Formatting instructions:

Do not enter dollar signs, percent signs, commas, X$,$ or any words in your response. Do not round any intermediate work, but round your $*$final$*$ response to $2$ decimal places $($example: if your answer is $12\mathrm{.}3456,12\mathrm{.}3456\%,$ or $$12\mathrm{.}3456,$ you should enter $12\mathrm{.}35).$