Rainey Company purchased a computer that cost $$45,000$ on June $31,$ Year $1.$ This computer had an estimated useful life of four years and a salvage value of $$1,000.$Rainey Company determines depreciation expense based upon the sum$$of$$years$$ digits method $($round all numbers to the nearest whole number and all percentages to the nearest $2$ decimal places$).$

On December $31,$ Year $2,$ the old computer is exchanged for a similar computer with a fair market value of $$22,000.$ Assume this transaction lacks commercial substance. Determine the recognized gain$/$loss on the trade $($if any$)$ assuming each of the following independent scenarios:

a$.$ Rainey Company paid $$5,000$ on the exchange

b$.$ Rainey Company paid $$500$ on the exchange

c$.$ Rainey Company received $$3,000$ on the exchange