Timothy can purchase a new car for $$35,000.$ Alternatively, in addition to a down payment of $$2,000,$ Timothy can make lease payments of $$350$ at the beginning of each month for three years to lease the car. The car has a residual value of $$17,500.$ Assume that the cost of borrowing is $3\mathrm{.}31\%$ compounded monthly.

In the lease option, what will be the buyback value of the vehicle at the end of two years?