I live in an apartment without washer connections. My wife and I spend about $40-$50 per month at the laundromat. That's enough money to pay off a new washer in a year.
There is lots of talk about attaching washers to faucets, but that doesn't allow for temperature control, or multitasking with the water.
I wanted a good, full size, intelligent washer that would be able to do hot and cold washes. I realized that the best solution would be to get at the water under the sink. It took a few trips to the hardware store to come up with the best solution, and it was such a simple one.
Instead of buying a Washing Machine Hose and finding fittings that would adjust the size down to what I needed, it turns out that a Dishwasher Hose is the perfect fit. So I just need to find the right splitter and I was in business.
I hope this answers your dreams of having a washing machine in a rental apartment, it sure answered mine.