An oil change requires — on average — 6 quarts of oil. That includes approximately 1 quart that is in the oil filter.
For several years, most manufacturers’ recommended oil change interval has been one year or about 10,000 miles, which ever comes first. This extended period is due to new oil technologies, clean burning, lead-free gasoline, and computer-controlled engine ignition.
The cost of an oil filter is about $5 to $7. The cost of a quart of oil is about $5 to $8. Both costs depend upon where the oil change is performed.
Therefore, not changing the oil filter might save about $13, about once per year.
If the filter is not changed, it will be required to perform beyond its design parameters and filter for many more miles and a much longer time. Also, the approximately 1 quart of oil not changed out because it is inside the old filter will be near useless in its lubrication work. Also, it will dirty the fresh oil added during the oil change process.
There is no reason to not change the oil filter.
In fact, there is every reason to change the oil filter each time the oil is changed.
You will prevent much extra engine wear by changing ALL the old oil and the filter each time.