350,000*0.01125 = 3937.5/yr in taxes. Lets just say $4000 although it might be a bit higher than that. On the property management cost you usually assume 8-10% but for $3K a month maybe you get a discount. Let’s just say $200/mo or $2400/yr. Vacancy/Maintenance tough to judge when you only have 1 property, but let’s just assume 1 month of rent per year.
So 36000-4000-2400-3000 = $26,600/yr. Cap Rate tends to be based on the value of the house but let’s calculate it both ways. For you the cap rate is 26,600/650,000 = 4.1%. For an investor it goes down a bunch because of the increase in the tax base. So a new investor that bought your property would have property taxes of nearly $8K a year putting the revenue down to 22,600. SO 22,600/700,000 = 3.2% Cap Rate. So there’s no investor demand for your house. Your potential buyer pool is limited to owner users. An owner user that bought at $700K and put 20% down is looking at a monthly nut of about $3500/mo which isn’t that much more than renting.
The problem you potentially face is that if/when interest rates go up and there’s other investments that look more attractive the costs for potential buyers are going to go up at the same time. I.e. when you can get a safe 4% return at a bank the mortgage rates will be close to 7% which makes the monthly nut close to $4500. In order to keep the monthly nut close to the $3500 @ 7% interest the home’s price would need to be around $500K rather than $700K.
If you’re betting or guessing that rates should rise in the near future than it would make sense to sell now. If you bet that rates will stay low for a long time than it’s better to keep the property and rent it out. If you use Japan as a guide than it’s probably better to hang on to it.