3,000/60,000 = 5% of the entire loan! I mean I get that it is a small loan so some things cant be helped (appraisals etc). But it is something to consider for sure. You are paying $3k for the privilege of borrowing money.
Ok so this is family members house got it. Issues to be concerned with are:
1. Tax implications, is this considered a (125-60) 65k gift from grandma to you? Would it be considered taxable?
2. Relatives. So grandma basically is giving you 65k, do you have to pay some of this windfall off to your relatives? Good chance they will see it as "the rich getting richer"
3. Property tax, not sure about your area but that might cause the auditor to start sniffing around due to the low sales price.
I might consider buying it cash, then refinancing if needed. My guess is you are a conservative investor which is of course fine. Going down to 5k in cash is a bit scary but investments always involve some level of risk. I assume by your handle you have a pretty safe job.
It would be a fine rental in the fact you would be cash flow positive.... BUT what everyone tends to ignore is the opportunity cost. You have tons equity day one. So say you make $8000 on it per year. Nothing to sneeze at but your paying cash you only get a 6.4% return, and financing the 60 puts you at a better cash on cash return but still lots of opportunity cost there.
Is there a sentimental attachment to grandmas house? Is flipping out of the question? Or even better living in it for 2 years and then selling to avoid all the capital gains tax. My experience with grandmas house is 5k of paint, a few new fixtures and appliances can go a long way.
TLDR version: Yes buy it, but there might be some negative externalities from the below market rate. I still want more info but understand if you dont want to share.