On a ranking point system, I need the sum of each rank to equal 100 and to gradually increase over 13 people?
Here is my problem:

There are 13 people who share a commission off of one big revenue pool.

Based on their performance, they are ranked #1 through #13.

Each of them takes a percentage of the revenue based on their ranking (#1 gets the biggest percentage, #13 gets the smallest percentage).

I want #1 to get 15%.
I want #13 to get 1%.

Is there a mathematical formula to figure out what percentage I can I can give to #2 through #12 in which the sum of all the percentages, including the 1% and 15% equals 100%?

It’s easy to get the numbers to distribute evenly from 1% to 15% using a contant rate of increase of 1.6666666% for each consecutive ranking but the sum of all the percentages equals 104%. Is there a parabolic way to figure out how to distribute the percentages?