I stated salary expectation below the range [CAN-BC]

[u/GovernmentLumpy8086]

Hi everyone!

I received a call after a final stage if interview at an investment bank from HR asking me to sign some personal data document and also dropping the question about the salary range I expected for the role. I flipped a question at HR asking for the range they had in mind but they said they did not know the range ( which is obv a lie ) and then I felt pressured into stating a lowest number since she asked for it and I ended up underselling myself low above the market rate. For reference I said 3k when the market range is 4-5k and might be more… I figured after doing the research. I made the mistake by not checking the salary range but this is a new industry for me so I had no idea and I am a fresh grad as well so some of my first formal negotiations too.

How likely is it they will be honest about it and give me 4k and how likely is HR is to just give me the 3k and call it quits?

Do i have any leverage in negotiating? How do i handle this situation so I at least get 3800/4000? Is there any remedyingw?