They pay first and security upfront and the last month in gradual payments in addition to the rent.

I didnt track it really, but i can tell you the calls flooded in for about one week after the mailers hit their mailbox...then faded gradually.

If we need to raise rent we do it gradually so they have plenty of time to make plans, which may include moving. 

I'm lobbying my husband that we should raise him to $650 as of January 1.My feeling is that if the tenant's unit is below market, but they're a great tenant, raise it gradually toward market, and consider that you'd probably lose a month if they leave, plus you'd probably have to recondition the unit. 

Should I up their rent gradually once I own it or just tell them the new rent and let them decide to stay or leave?

California had around 15k borrowers, but not all that number is a tier 1 mod, many states didn't even make it to 200 borrowers.The adjustment is a gradual step up to current prevailing rates year over year.  

As a 19 year old currently enrolled into a community college, my desire to beginning a career in real estate has gradually increased and has even led me to this community.

Zero-interest-rate policy is over but the increase will be gradual.

when filling a vacancy do you stick right at market rent then gradually go down in price if no interest?

If it were me, I would proceed with some gradual increases, and maybe pair that with some niceties - i.e. address some maintenance the previous landlord was deferring, a fresh repaint of a room or two, etc.