DTI includes loans and obligations. For a mortgage origination they like to see 6 months cash in reserves post close. DTI 50% is about the absolute limit they'll allow for taking on more debt.
If DTI limits are a concern and you want to take 15k then you'll want to seek a lower payment. The question I would also present to you is did you make a significant down payment? How much was your apprasial over what you currently owe? If there is already 15k in the property you might be as well off taking a HELOC or a Home Equity loan out.
Then with a HELOC or HE you will get a lower payment with a 20 or 30 year repayment as opposed to 10 or 15. You can also seek out an interest only payment to reduce that number even further. You can write home equity interest off your taxes if 1) the total house backed debt is lower than 750k, 2) all of the money in th equity loan will be spent toward home improvement and you can back it up with receipts. Basically you can get the same write off that you normally would with a business loan with this exclusion.
The payment on 15k on a 7% interest only equity loan with a 20 year no interest period is only $87.50 and you can in your tax bracket write off a quarter of that so like for a net of $65 dollars you could have this loan.
https://www.calculatestuff.com/financial/interest-only-calculator
If instead you wanted to take out a personal loan and I can tell you from experience Lightstream has one of the best home improvement rate in the industry at 15k they will charge you $226 for 84 months on a home improvement personal loan. Average lender probably $350 for 15k.
For the equity though it might require a 100% LTV lender for you to pull a substantial amount of equity out. Also with the 15k amount you are planning to spend are you sure you really need 15k? You may want to give it 6 months to bring in the estimates before you know exactly what you might need.
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