Freedom Day

It's the $4$ th of July, so to be very patriotic, you decide to invest </code>b_0$ in a stock today that doubles in value each day, and then drops the total account value by </code>r$ immediately after each doubling. For example, if $r = 40$ and $b_0 = 100$ , you would have $$160$ in your account tomorrow. You find that after $n$ days, you have $$0$ in your account. How much money was in the account $0 \leq k \leq n$ days after your initial investment? Report the answer with $r = 1280, n = 8$ , and $k = 5$ .