Ponzi Scheme Calculator

Question

I'm trying to write a Efficient Ponzi scheme calculator that when given: the initial amount invested, a maximum number of recruits that a recruiter may have, the entry fee and the percentage of the entry fee each recruiter can keep. It returns a minimum number of persons that must be recruited for the initial investment may be recouped.

• n: the number of dollars invested

• b: the maximum number of recruits that a recruiter may have

• m: the entry fee

• r: the percentage of earnings each recruiter is allowed to keep.

Here is the Code I have written:

def findNumPersons(n, b, m, r):
    initial_earn=b*m
    i=0
    custom_earn=m*(r/100)
    ans_returns=m-custom_earn
    recruits=0
    counter=1
    while(i<n):
        i=initial_earn+(recruits*ans_returns)
        counter+=1
        recruits+=1
    return counter

My challenge is that as n get larger and (b,m,r) get smaller it takes longer to calculate the minimum amount of persons.