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I am playing a game in which I have a starting amount of money, which I am calling x. I currently earn interest at a rate of 5% per day, and I gain 150 dollars every 12 hours. If I pay 100,000 dollars for a better interest/income plan, then my interest rate changes to 15% every 20 hours, and I get 300 dollars every 6 hours. I want to know at which value of x I should buy the better income/interest plan, in order to maximize my total bank balance in the long run. If it makes things any easier, I would not mind assuming that the 15% interest every 20 hours happens every 24 hours instead. (Side note: I plan to repeat this for another income/interest plan later on, which costs 500,000 dollars, delivers interest at a rate of 25% every 12 hours, and gives me an income of 500 dollars every 3 hours.)

My biggest issue here, with my method, was that I had two variables. I set the number of days after earning x dollars to n, which is really confused, obviously. Anyways, I'm gassed for sleep so my brain rolled over and died and here is my plea for help :).

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