Help understanding and selecting a statistical process

I must first confess that I am not a student or department head. I’m someone that likes to work statistical problems and educate myself wherever possible.

I have been endeavoring to develop a program in Microsoft excel to determine when an individual participating in a random selection process could expect to be selected if at some point in the future that happening is guaranteed. After each attempt, the individual is moved up one level where they will be selected before anyone at a lower level. However, the guaranteed level also increases by “x” amount each time. For example im currently working with the current guaranteed level is 24 and the individual catches up 1 level every 12 attempts (x=0.083). Obviously, for an individual participating for the first time, by the time they have gone through 12 selection processes, the guaranteed level would have increased to 35, and 24 attempts to 46. Using this example, what statistical function would I use to determine the level at which the individual will catch up to the guaranteed level?

Thank you so much for any help offered.