PITI is an acronym for the expenses accompanying a property. They stand for:
P = Principal. The portion of your loan repayments that go to the principal amount you borrowed.
I = Interest. The portion of your loan repayments that go to interest.
T = Taxes, rates or levies imposed by government bodies. e.g. Council Rates, State Taxes, Land Tax.
I = Insurance. The cost of insuring your property.
P + I + T + I = PITI.
For a loan to be considered affordable, monthly PITI on any one property must be less than 28% of your monthly gross salary. ('Gross' meaning 'pre-tax', not 'massive', unfortunately.)
Furthermore, monthly PITI combined with other monthly debt payments should be less than 36% of your monthly gross salary.
28%, 36% gives us the 28/36 rule that banks use to work out if you can afford the loan you are applying for. Centuries of lending has taught banks that anything on the wrong side of these magic numbers has a far greater chance of becoming a bad loan. If they turn you down, it's for a good reason. Ignore them at your peril!
" ... and they said I could have more!"
Banks don't have to use the 28/36 rule. In fact, it's very tempting for them to lend greater amounts that take you longer to repay because they will collect more interest. But the more they lend, the greater the risk you cannot repay. It depends on how much they're willing to gamble.
If you look hard enough you will find a lender for any set of circumstances. But if the conservative banks won't touch you then your choice may be restricted to lenders on the 'fringe' - including boutique banks - that make you pay for their risk in the form of higher interest, fees, or reduced facilities.
Or you could be right. This maths could be pure bollocks. It just doesn't take into account that your ship's about to come in. If the banks are too short-sighted, go see 'Arry round the front bar of the Winchester. Tell 'im I sent ya.
Oh, and mind your knees and elbows.