An easy way to make money by maximizing deposits from new tenants:
You need at least 1 big apartment for rent and any other (cheaper) apartment to relocate people to.
1.Decorate a big apartment to get as highest rent as possible
2.Recruit tenants for apartment, select the tenant with best stats or biggest deposit (depends what you are after)
3.Relocate recruited tenant to cheaper apartment (costs 5 tickets)
4.Recruit another tenant for the big expensive apartment, relocate and repeat as long as you have (empty) apartments for rent
5. (Note: Tickets are rare so think before you make a choice.)
6. Marry another existing tenant. It frees an apartment to be rented out for another deposit. You can try to mate them by placing a bench near their apartments.
This way you get the maximum deposit when you get new tenants, just keep relocating them until you have no more free rooms left.
DO NOT ask a hired tenant to leave, this will cost their deposit +10%. This is the downside of this "trick", so make sure you actually want to keep the residents you hire (hence the select stat remark at step 2).