Optimal reward reinvesting interval with non-zero transaction fee

Question

Description of the system

I have a system where every interval of time (lets assume every day) a reward (n) is paid out.The amount n paid out every day/interval is constant. (i.e n=20$)

I have the option of claiming the reward, which has a fee for every withdrawal. (i.e fee=0.40$)

Once claimed the amount n can be reinvested and gain a yield y per interval. (i.e y=0.2/365)

Problem

Obviously claiming the reward too often will diminish the total yield. But also never claiming the reward will result in missed opportunity since reinvesting would give a yield 1+y. I am looking for the optimal number of intervals between each rewards claim and reinvestment.

Possible solution

I wrote a piece of code in python that supposed to solve this problem, but when trying to come up with a mathematical formula to validate the code I was stuck. In short, the function runs a simlation for d days, does the claim+reinvest procedure every restake_interval days using a modulo operator, and returns the amount accumulated at the end of d days.

def restaking(restake_interval, n, y, fee, d):
    # restake_interval: interval between each reinvstment
    # n reward amount on each interval
    # y interval yeild %
    # d days/intervals to run the simulation for
    available = 0  # amount available for withdrawal in the system
    amount_staked = 0 # amount already invested that's gaining yield
    for i in range(d):
        available += n
        if (i+1)%restake_interval == 0:
            # claim and reinvest
            amount_staked += available-fee
            available = 0
        amount_staked *= 1+y
    return amount_staked+available

By running this function in a loop like this I was able to find the optimal restaking interval. But I am unsure of the result.

# find best restake day interval
n=20
interval = 1
prev_result = -1
while True:
    result = restaking(interval, n, 0.2/365, 0.4, 365)
    if result < prev_result:
        break
    interval += 1
    prev_result = result
    
print("\nSOLUTON: restake every {} days: {:.2f}$ gain at {}days".format(interval-1, prev_result, 365))

You can run this code online at https://www.tutorialspoint.com/execute_python3_online.php

Question

What is the mathematical formula/model for solving this problem? Is the logic behind the code correct?