After deciding to acquire a new car, you can either lease the car or purchase it on a two$-$year loan. The car you wish to buy costs $$31,500.$ The dealer has a special leasing arrangement where you pay $$92$ today and $$492$ per month for the next two years. If you purchase the car, you will pay it off in monthly payments over the next two years at an APR of $5$ percent. You believe you will be able to sell the car for $$19,500$ in two years.

a$.$ What is the present value of leasing the car? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What is the present value of purchasing the car? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$

What break$-$even resale price in two years would make you indifferent between buying and leasing?