You are purchasing a car for $$12,465\mathrm{.}00$ plus $5\mathrm{.}65\%$ sales tax. You make a $$1,300\mathrm{.}00$ down payment and have a fair credit score $($interest rate $6\mathrm{.}40\%).$ How much interest is due at the end of the first month? If you improved your credit score to good $($interest rate of $5\%)$ and paid $$1,500$ on your purchase, how much interest could you save in the first month?