3. At time t = 0, Karl buys three perpetuities which pay according to the following. (i.) Perpetuity X pays 1 at times 2, 4, 6, 8, 10, 12, .... (ii.) Perpetuity Y pays 2 at times 3, 6, 9, 12, 15, (iii.) Perpetuity Z pays 3 at times 6, 12, 18, 24, 30, Suppose the annual effective interest rate for all three perpetuities is i > 0. (a) Write an expression for the total present value of the three perpetuities that is entirely in terms of interest functions at an annual effective interest rate i. (b) Compute the present value for i = 5%, 10%, 15%, 20%, 25%. 3. At time t = 0, Karl buys three perpetuities which pay according to the following. (i.) Perpetuity X pays 1 at times 2, 4, 6, 8, 10, 12, .... (ii.) Perpetuity Y pays 2 at times 3, 6, 9, 12, 15, (iii.) Perpetuity Z pays 3 at times 6, 12, 18, 24, 30, Suppose the annual effective interest rate for all three perpetuities is i > 0. (a) Write an expression for the total present value of the three perpetuities that is entirely in terms of interest functions at an annual effective interest rate i. (b) Compute the present value for i = 5%, 10%, 15%, 20%, 25%