Suppose that the interest rate follows the following stochastic process: drt = (1 rt)dt + e-dBt, where ro = 0 where B+ is a standard Brownian motion. 3a. (10 points) Denote Rt = etrt. Using Ito's lemma, find the expression for dRt. 3b. (10 points) Solve for Rt and then rt. In your answer, Rt and rt should be written as a sum of a deterministic term and an Ito integral. 3c. (10 points) Calculate E[rt). When t approaches infinity, what does E[rt] approach to? Please show your work. 3d. (10 points) Calculate Var(rt). When t approaches infinity, what does Var(rt) approach to? Please show your work. Suppose that the interest rate follows the following stochastic process: drt = (1 rt)dt + e-dBt, where ro = 0 where B+ is a standard Brownian motion. 3a. (10 points) Denote Rt = etrt. Using Ito's lemma, find the expression for dRt. 3b. (10 points) Solve for Rt and then rt. In your answer, Rt and rt should be written as a sum of a deterministic term and an Ito integral. 3c. (10 points) Calculate E[rt). When t approaches infinity, what does E[rt] approach to? Please show your work. 3d. (10 points) Calculate Var(rt). When t approaches infinity, what does Var(rt) approach to? Please show your work