TP $($a real estate developer$)$ has subdivided a large tract of land, installed water and sewer lines and the necessary roads, He has sold one of the subdivided lots in $2022$ for $$200,000.$ He has computed his basis in that lot to be $$50,000.$ The buyer has agreed to pay the $$200,000$ in installments, calling for $$50,000$ in $2022$ and the balance in $3$ equal annual installments plus interest at $5\%$ per annum on the unpaid balance to be paid annually with each principal payment. Assuming the buyer makes the $2023$ payment at the end of the year, how much income will be recognized by TP in $2023?$

a$.$ $$7,500$ in interest income only

b$.0$

c$.$ $$37,500$ in gain, plus interest of $$7,500$

d$.$ $$12,500$ in gain plus interest of $$7,500$

e$.$ None of the above