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(in nyc, to wash on warm cycle)   Cost of washer / dryer is $1,000 to 2,000 dollars and should be good for at least 25,000 lbs of laundry or $2 to $4 dollars per 50lbs.   total $9 (high efficiency models) to $12 dollars to do it at home.
When washing clothing at home, consumers pay about 36 cents for the energy to run the washing machine for one load of laundry, 40 cents for energy for the dryer and 11 cents for water. The estimate does not include cleaning products or equipment costs. The average cost of a washing machine is about $700. It has a lifespan of about nine and a half years, assuming that one load of clothing is washed per day. A dryer costs about $600 and lasts about 11 years. Based on the savings by washing at home versus at a laundromat, it takes about 610 loads of laundry to recoup the cost of purchasing a washer and dryer.