1. At time t=0,$30 is deposited into each of Fund X and Fund Y. Fund X accumulates at a nominal rate of discount of 10% per annum convertible semiannually. Fund Y accumulates at a nominal rate of interest of i(4) per annum convertible quarterly. At time t=10, the accumulated value of Fund X equals the accumulated value of Fund Y. Calculate i(4). Show your work. (5 marks) 2. Mary age 30 today contributes an amount $X at the end of each month into a fund which earns a nominal rate of 12% convertible monthly. Starting age 65 , she will use the entire account balance to purchase an annuity at a nominal rate of 8% compounded semiannually, which will provide $500 at the end of each month to her for twenty years. Calculate $X. Show your work. (15 marks)