# Thread: Differential Equation for Continuously Compounded Interest

1. ## Differential Equation for Continuously Compounded Interest

How do I use differential equations to get

dM/dt = r(t)M(t)

to equal to

M = E.e^[-(integral from T to t) of r(s)ds]

Where r is the continuous compounded interest which is a function of t and E= M(t) and theT represents some future time.

Where did the ds come from or the r(s) for that fact

2. The r(s) and the ds both come from being "dummy" variables. What you're doing here to solve the problem is separating the variables: divide both sides by M(t), and then integrate w.r.t. t. The integral on the RHS is equivalent to an indefinite integral w.r.t. t.

Does that make sense?

3. Ahhhhh Yeah I see how it's done THANKS a lot!

4. You're welcome!