Problem 3 (10 pints). Assume dSt = 0+Stdt + 04StdWand the interest rate (Rt) te[0,1] is non-random but time-varying (i.e., a function of t but independent of w). We have a contract that pays $1 at time T (i.e., a bond with face value $1 and expiration at T). Find the price of the contract at t = 0. Support with reasoning (such as indicating which formula/theorem you are using); a final answer alone will lose at least half credit. Problem 3 (10 pints). Assume dSt = 0+Stdt + 04StdWand the interest rate (Rt) te[0,1] is non-random but time-varying (i.e., a function of t but independent of w). We have a contract that pays $1 at time T (i.e., a bond with face value $1 and expiration at T). Find the price of the contract at t = 0. Support with reasoning (such as indicating which formula/theorem you are using); a final answer alone will lose at least half credit