Here are my thoughts on some of your questions:
1) If both of you are going to be on the heloc, then yes, you would need to include your wife's income.
2) When calculating your DTI ratio, their reference to mortgage is PITI (so principal and interest - i.e. mortg- plus taxes and insurance). So if your mortg is 1300 and taxes are 400, they are going to add those up for your DTI calculation (as well as insurance).
3) In terms of calculating your rental income, you are definitely going to have to disclose that you have rental income. Typically, they are going to take 75% of the rent and offset that against your PITI on the rental and thats your net profit or loss.
So here is how they're supposed to calculate your DTI:
1) Add up your monthly income from jobs - both yours and your wife's and this goes to your INCOME side.
2) Add up all the minimum loan payments on your student debt, credit cards, car loans, etc. Plus add up your PITI on your primary residence. This goes to your DEBT side.
3) Lastly, they will take 75% of the rent from your rental income and subtract your monthly PITI on your rental property(ies) and if its positive, that positive number will be added to your INCOME side. If its negative, that negative number will be added to your DEBT side.
i.e. Lets say you have two rental properties that rent for 1k apiece per month. Thats rental income of 2k times .75 or 1,500/mo. Then lets say your mortgage payments on those two houses (including taxes and insurance) comes to 1400/mo.
You would take 1,500 and subtract 1,400 and get a positive 100/mo. That 100/mo would be added to your INCOME side.
4) They will then take your DEBT number and divide by your INCOME number. So lets say you had w2 income of 9,900/mo and you had 100 in rental income. That would give you 10k/mo INCOME.
Then lets say you had PITI on your primary residence of 1700/mo plus another 2300/mo in other credit card, car loan and student debt payments. That would be 4k/mo DEBT payments.
4,000/10,000 = DTI ratio of 40%. You qualify.
@Mike H. Great break down and examples!
The bank will typically want copies of your W2's and bank statements from other accounts they don't hold. Your wife doesn't have to be on heloc but will have to sign some paperwork because you are married. You might need a copy of your lease on the rental. My bank didn't use any income from the rental. You should get better rates and LTV when using your primary house for the heloc vs using your rental property. It may be worth paying for the full appraisal to be able to maximize your heloc value.
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