Madisyn negotiates a purchase price of \(\$ 45,800\) for her new car. The sales tax in her area is \(7.25 \%\). Her license, plates, and registration come to \(\$ 199.00\). The dealership charges her a \(\$ 1,000\) destination fee and a \(\$ 275\) processing fee. How much will she finance in total for the car?

Find the total cost to purchase the car.