A financial differential equation

[simpleuser]

Homework Statement

Express the following function into terms of t.

$$\frac{\Delta CF}{\Delta T} = C \cdot \Delta T \cdot \frac{1}{(1+r)^t}$$, given CF(T) = 0.

Homework Equations

None.

The Attempt at a Solution

As I am not a mathematics student, I am not able to solve these kind of differential equations. I can only solve first degree differential equations. Therefore I would like to ask a few questions about this.

a) Is this solvable? (By hand or using Mathematica / Maple)
b) Can someone provide a hint how to start solving these equations? (Actually I do not need to solve this manually, I only need the solution.)

Information: this equation does not come from a textbook or is a homework assignment. It's just pure of interest composed by a friend of mine.

If this question is not on it's place, I am sorry for asking. Thank you for your time and effort.

 

[LCKurtz]

Homework Statement

Express the following function into terms of t.

$$\frac{\Delta CF}{\Delta T} = C \cdot \Delta T \cdot \frac{1}{(1+r)^t}$$, given CF(T) = 0.

As written, that isn't a differential equation and I can only guess what you mean. I suppose CF is the unknown function (I'm going to just call it f not to confuse it with C, which I suppose is just some constant, or is it also supposed to be CF?). So perhaps you mean this differential equation:

$$\frac {df}{dt} = C\cdot \frac{1}{(1+r)^t}$$

but I can't make out the meaning of the $\Delta t$ on the right side. Also your initial condition doesn't make sense, maybe f(0) = 0? A little clarification please.

 

[simpleuser]

Well, it means the following. The T is the variable of the function and $$\Delta T$$ means the change in the variable. $$\frac{\Delta f}{\Delta T}=\Delta T \cdot C \cdot \frac{1}{(1+r)^t}$$, does it mean that is not solvable with the $$\Delta T$$?

If this is not a differential equation, can I replace $$\Delta T$$ with something else? It means the change in the variable of the function that we do not know.

 

[gomunkul51]

I think it is better for all of us if you tell in detail the problem in words you want to "model" by a differential equation and we will try to write a proper DE.

On the other hand if the equation is given like this, may be deltaT could be written as the difference of some initial T₀ and T which is the variable?
also, r is a constant? and f (=CF) is only a function (depends) on T?

P.S. Happy new year ! :)