Say you have a bank account in which your invested money yields 3% every year, continuously compounded. Also, you have estimated that you spend $1000 every month to pay your bills, that are withdrawn from this account.
Create a differential model for that, find its equilibriums and determine its stability.
My problem here is that the \$1000 withdrawal is not continuous on time, it's discrete. The best I could achieve is, if $S(t)$ is the current balance: $\dot S (t) = 0,0025S(t) - 1000$. I'm using $0,0025$ as the interest rate because it yields 3% every year, so it should yield 0,25% every month. But I'm pretty confident that it's wrong. Any help would be highly appreciated! Thanks!