If you have a bank account with zero balance and are given $200 to start it on day one and each day after you are given the balance + $5.00 how long will it take to have the sum of $10,000.

Is there interest to be figured in?

No, I used bank account and payments for simplicity sake.

It's easier to simply calculate the balance on day 1, day 2, day 3 etc until you reach $10,000 than it is to derive the formula (it doesn't take very many days). But if you actually need the formula, I suggest considering the doubling of the original $200 each day as one part of the problem and the doubling of the $5 each day after day 1 as a separate part, then add them together. Go ahead and try this, and post back with your attempt and we'll check it for you.