Modelling interest with differential equations (Interpretation) I am having trouble interpreting the meaning of this differential equation model for interest on an account. The problem is as follows:

Assume you have a bank account that grows at an annual interest rate of r and every year you withdraw a fixed amount from the account (denoted w). Assuming continuous compounding interest and continuous withdrawal, the described account follows the differential equation:
${\frac{dP}{dt} = rP - w}$
Where P(t) is the amount of money in the account at time t.

I am confused as to why we subtract the entire amount ${w}$ in the equation? My interpretation (which is obviously incorrect) is that ${\frac{dP}{dt}}$ is the change in the amount of money in the account with respect to time for any given time ${t}$. If this is so, wouldn't the above equation mean that at every instant ${t}$ we are adding ${rP}$ to the account and subtracting the entire annual deduction ${w}$ so that at the end of an entire year we've deducted more than ${w}$ from the account?

$w$ is the (continuous, constant) rate of withdrawal, and $rP$ is the (continuous, proportional) rate of interest accrual.
