Problem 4 (Required, 20 marks) We consider a 3-year continuous annuity which pays continuously at an annual rate of f(t) where f(t) = max(4,t?), t > 0. It is given that the money grows at a force of interest of (0.03 if t31 0 = 10.05 if t > 1% Calculate the present value of this annuity. Show all details. (Hint: Find the accumulation function a(t) first.)