# Differential Equations - with

1. Feb 9, 2009

### 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.

2. Feb 9, 2009

### HallsofIvy

Staff Emeritus
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
$$\frac{dA}{dt}= rA- 200$$