Be careful about renting or investing with friends or relatives.
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So, if we choose to "split" the house, and each put up 1/2 the down ($25,000 each), and 1/2 the mortgage ($1500), and 1/2 the HOA ($150).... seems fair... until... they live there...
We are both shelling out $1650/month, and they live there, they are getting a better deal. So, I "charge" them rent?
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The answer is that which both parties agree. There is no guideline or rule.
I don't think you should pay for the mortgage (part or all). Why not keep it simple? If you put a down payment, agree to a net return on the down payment. If you put down $25k, ask for an annualized return of 8%, 10%, 18.99%, or whatever floats your boat. Just be aware that if all he!! breask loose, you may very well lose your entire investment, even if the he!! is brought by the relatives.
In my opinion, your plan is bordering on speculation. Basically, your investment is dependent on appreciation to cover the monthly interest payments.