Contest Prize Distribution Formula

Produce a formula that calculates a cash prize distribution among the top x% (example: 30%) of the participants who are entered into a contest. The mathematical formula will be used to determine the payout at each place (1st, 2nd, 3rd, … nth). However, the distribution needs to deliver a greater cash prize towards the top for the higher finishing participants. The formula is for a progressive jackpot tournament. For any one tournament, there may be 100-10000 persons, with payouts from $50 - $50000 and places from 1st to 1000th place. Input variables: a = payout amount ($) p = percentage of participants that receive payout (%) n = number of participants in the tournament f = fraction that the payout will reduce from one participant to the next ( not sure because it may vary; open to suggestions )