a ) Ishan and Hazel plan to retire at age 60 with a retirement income of $48,000 a year from their savings. Rather than pay themselves the whole amount at the beginning of each year, they have decided that payment at the beginning of each quarter of $12,000 gives them the right balance of flexibility and maximized interest earnings. They feel they can safely earn an interest rate of 6.5%, compounded quarterly, on their money and they are budgeting based on the prediction that they will live until they are 90 years old. How much money will they have to have saved by the time they are 60 in order to reach their retirement goal? If the same total calculated above was to be saved, but no interest earned whatsoever, how much would be available to live on each quarter? If the full 30 years are lived and quarterly budget spent, how much money in total will have been utilized in retirement? How much will have been earned in interest?

b) : Now that Ishan and Hazel have their saving goal calculated they want to start budgeting to reach that goal. They are 40 years old, so they have just 20 years to save up the total they calculated they would require so that they can still reach their goal of retirement by age 60. If they assume the same interest rate, and make deposits into their savings at the beginning of every month, how much would their deposit have to be each month? How much interest will be earned?