2. I borrow Pg dollars from a lender at a per annum inter-It rate of r compounded continuously. I pay my loan o' continuously at a constant rate of k dollars per annum. (a) (12 points) If POE) is the money I owe in dollars as a function of time I? (measured in years), set up the initial value problem for which PU?) is the solution. Then solve this problem, express~ ing Pb?) in terms of PD,t,r and k. (b) (8 points) What should It be if I need to pay my loan off in T years '3' Express your answer in terms of P0,? and T