Continuous Compounding with Withdrawals: Solving for Amount in an Account

[atesme]

1. Assume that y₀ dollars is deposited in an account paying r percent compounded continuously. If withdrawals are at an annual rate of 200t dollars (assume these are continuous), find the amount in the account after t years.
2. continuously compounded interest: A(t)=A₀*e^rt
3. I have no idea how this works at all. The part that's throwing me off is that the input (200t) dollars affects the interest, and I don't know how to include that in the equation.

 

[HallsofIvy]

Money in the account is increasing due to the interest earned: rA "dollars per year". Money in the account is decreasing due to the money with drawn, 200 "dollars per year". Therefore the amount is changing at any instant by rA- 200 "dollars per year". The rate of change is, of course, dA/dt so your differential equation is
\frac{dA}{dt}= rA- 200