Problem:

Samuel is going to retire in 20 years. In order to live comfortably, he thinks he will need to withdraw $120,000 every year during retirement. These annual withdrawals will be made at the end of each year during retirement. Sam believes he will live for 30 years after he retires. During retirement Sam will earn 4% per year compounded annually.

In addition to the annual annuity, Sam would like to receive an income of $9,000 per month, at the beginning of each month for the first year of his retirement.

Sam wishes to set up a scholarship at Ryerson University. The scholarship will make an annual payments to one Ryerson student. The first payment from the scholarship will be made 4 years after Sam retires. Payments will then be made every year after that in perpetuity. The first payment from the scholarship will be for $25,000. The payments will increase by 1% per year.

Sam has set up a retirement savings account. The account earns 8% per year compounded quarterly. There is $15,000 in the account today.

If necessary Sam has decided to set up a new savings account. The new account earns 6% per year compounded annually. Sam will make weekly payments into the account until he retires. The payments will be made at the end of each period.

1. 1. a) (5 marks) How much money does he need when he retires to fund: his retirement income during the first year of retirement; the annual annuity; and the scholarship?
2. 1. b) (2 marks) How much money will he have in his retirement savings account when he retires?
3. 1. c) (3 marks) What will be the amount of the weekly payments to the new savings account that is needed to finance the shortfall? If you believe that there is no shortfall, you are to assume that shortfall is $1,000,000.