# Compound interest using DE

1. Nov 8, 2012

### Haethe

1. The problem statement, all variables and given/known data

Assume that Po dollars is deposited into 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.

3. The attempt at a solution

I have two differential equations, but I'm not sure which one will work:

dp/dt= rP+200t

Or,

dp/dt = rP +200

My first choice was the 1st one, but I searched the question on google, and people said that the DE is the second one. Can you tell me the correct equation, and explain why?

Last edited by a moderator: Nov 9, 2012
2. Nov 9, 2012

### Ray Vickson

If B(t) is the balance at time t (that is, the amount in the account), look at what happens over the short time interval from t to t + Δt. How much money is withdrawn in time Δt? How much interest es earned in time Δt? What will be the new balance B(t+Δt) at time t + Δt?

Working carefully through the details like that is the way to ensure getting the correct DE.

RGV