How Do You Model Compound Interest with Differential Equations?

[Haethe]

Homework Statement

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.

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?

 

[Ray Vickson]

Homework Statement

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.

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?

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 How much money is withdrawn in time Δt?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