V=(c/r)(1-e^(-rt))+e^(-rt) I believe I need to take the partial derivative with

Question

V=(c/r)(1-e^(-rt))+e^(-rt)

I believe I need to take the partial derivative with respect to c, r, and T, but I am not sure what I should do with it afterwards in order to prove the change.

(a) how does V change as c, r and T each change (i.e., 2 held fixed and the other allowed to change)? (b) What happens as T +w, and the bond becomes perpetual? (c) Where in the calculus used to derive Expression 4.6 is the assumption that there is a constant valuation rate r used? Derive the above three ((a)-(c)) results. (Specifically, you need to mathematically justify your conclusions, in each.)

Explanation / Answer

Consider the function:

                       

Partial differential the given function.

                 

               

               

If , then

         

        

           

In the question, not specified about expression 4.6, so unable to answer for subpart (c )

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