You are purchasing a new car toyota rav $4,$ purchase price is $$31,548.$ Consider instead that you will make only a $$1,000$ down payment. If you do this then the interest rate on the loan will increase to $1\mathrm{.}75\%$ per month. However, for this unique loan you will pay $$250$ at the end of the first month and then will increase the amount that you will pay by $$50$ each month $($i$.$e$.$ each payment is $$50$ more than the previous month's payment$)$ for the next $36$ months. If you were to accept this plan, would you have paid off the entire finance amount of the loan? That is$,$ what is the difference between the present value of the amount paid and the present value of the loan's finance amount?