The answer
AC/Heat Pumps last 12-15 years; Gas Furnaces last 15-20 years. Apply the $5,000 Rule: Repair Cost x Age in Years; if > $5,000 (e.g. $600 x 10 yrs = $6,000), replace. Replace if major components fail (cracked heat exchanger, locked compressor) or if using obsolete R-22 refrigerant.
Sources
This answer is drawn from the standards and guidance below. It is general information about how these systems work — not a diagnosis of your property.