Do you ever rescind a offer to a tenant of a rental and why?

[Colleen F.]

 Ok so  I offered a property to a group of 3 younger female tenants whose landlord references were very good.   I was upfront about everything in terms of pre-paid rents security deposit etc.   I send them the deposit info and put in dates for the deposits to be paid. They want occupancy May 1.  So basically they need to give at least half the money next week and all of it before  occupancy.  They call me back and say I never expected that soon can we pay it over time with the rent and that is illegal in RI to ask for that much upfront (it isn't  I know exactly what I can do).  I say "no"  they call back and say ok I can come up with the money. There is a  holding deposit form for them to sign and send the deposit and they say can you sign it first.  I am thinking  to rescind due to all the  negotiating. have your  rescinded an  offer on  a place in this kind of situation? If so why?