Your younger brother is celebrating his 30th birthday and wants to start saving immediately for his retirement at age 60. He tells you that ideally he would like to withdraw $50,000 the day he turns 60 years old until the day he turns 80 years old. He says that he would be comfortable putting aside some money each year in an annuity and believes that he would be able to earn 6% rate of return. i. How much money would your brother have accumulated at the age of 60 in order to finance her $50,000 per year during her post retirement? (5 marks) ii. iii. iv. V. If your brother starts making annuity payments to his savings accounts when he turns 30 years old and she will makes her last deposit at the age 60, how much must she deposit each year starting age 30? (5 marks) Taking into information in part ii, how much must he deposit each year until he reaches age 60 when your brother mentions that he also has a savings account of $25,000 to start the account? (5 marks) Your parents bought your brother a life insurance policy that matures on his 50th birthday for which your brother will receive an amount of $50,000. If he add that to the retirement fund, how much must he deposit each year until she reaches age 60? (4 marks) Briefly explain what nominal rates, periodic rates and effective rates are and give examples on when those rates are being used. (6 marks) (Total: 25 marks)