4. (a) Show that for k, n = 1, 2, 3, 4, .... = a kni =k](1+i)"-1 anli (b) A 40 year annuity due has payments of 5000 once every four years. A 40 year annuity immediate has payments of 1300 at the end of each year. Suppose the two annuities have the same present value and that both of their present values are calculated according to an annual effective interest rate of i. Find i. 4. (a) Show that for k, n = 1, 2, 3, 4, .... = a kni =k](1+i)"-1 anli (b) A 40 year annuity due has payments of 5000 once every four years. A 40 year annuity immediate has payments of 1300 at the end of each year. Suppose the two annuities have the same present value and that both of their present values are calculated according to an annual effective interest rate of i. Find