On first blush I’d say no, don’t do it.
$370K for effectively a 3 unit, or $123K/unit. That’s a lot. For $38,400 in annual gross scheduled rents, the 2% rule would value this at $160K (but, it doesn’t sound like war zone or low income, so the 2% rule is not a very good guide here).
On second blush, applying the 50% rule, this 3 unit is essentially break even.
Scheduled Gross Income (SGI or Rents) $38,400
Operating Expenses (@50% of Rents) ($19,200)
Debt Service (PI) ($19,843)
Annual Cash Flow ($643)
But there is still that pesky fourth unit, and the operating expenses it will consume. So, it is far from free rent.
From a different perspective, the analysis of renting all four units, assuming for example purposes, that fourth unit would rent for $1,200 per month:
Scheduled Gross Income (SGI or Rents) $52,800
Operating Expenses (@50% of Rents) ($26,400)
Debt Service (PI) ($19,843)
Cash Flow $6,557 ($137/month/unit)
So, there is your rent charge (opportunity cost). $6K/year NOT in your pocket.
If you can really get a 3.75% loan with a LTV of 96.5%, good deal. I'd work on that sales price, though, and get it down as much as possible.
My opinion is you’re accepting a high price, and it only appears to work (with all units rented) because it is offset by a low interest rate.
If the interest rate you mention is an ARM, forget it.