(Continuously Compounded Spot Rates and Instantaneous Forward Interest Rates): Suppose that the spot rates are described according to a continuous compounding convention so that the discount factors are given by d(t)=etr^c(t). We assume that the function r^c is defined on (0,) and differentiable. (a) Given 0 and T>, let 0,,Tfor denote the continuously compounded interest rate agreed upon at time 0 for an investment or loan to be initiated at time and settled with a single lump sum payment at time T. If the amount to be invested at time is V() then the value of the investment at time T will be V(T)=V()exp[(T)0,,Tfor]. Find an expression for 0,,Tfor in terms of ,T,r^c() and r^c(T). (b) Express limT+0,,Tfor in terms of ,r^c(), and r^c(). (The value of this limit has a special name. It is called the instantaneous forward rate at time as seen from time 0.) (Continuously Compounded Spot Rates and Instantaneous Forward Interest Rates): Suppose that the spot rates are described according to a continuous compounding convention so that the discount factors are given by d(t)=etr^c(t). We assume that the function r^c is defined on (0,) and differentiable. (a) Given 0 and T>, let 0,,Tfor denote the continuously compounded interest rate agreed upon at time 0 for an investment or loan to be initiated at time and settled with a single lump sum payment at time T. If the amount to be invested at time is V() then the value of the investment at time T will be V(T)=V()exp[(T)0,,Tfor]. Find an expression for 0,,Tfor in terms of ,T,r^c() and r^c(T). (b) Express limT+0,,Tfor in terms of ,r^c(), and r^c(). (The value of this limit has a special name. It is called the instantaneous forward rate at time as seen from time 0.)