You acquire a 30-year mortgage with a fixed monthly compound interest rate of 0.29% to purchase a house that costs $250,000. In addition to the regular monthly mortgage payment that the lender requires, you decide to pay an additional $50 each month starting with the first payment. What is the total number of payments (full and partial) you will make now, and what is the amount of the final payment? Carry as many digits forward as possible during your calculation.