Michael Piemontese is 50 years old and would like to retire at age 65. He currently earns $55,000 per annum. He pays tax at an average rate of 18% of his gross income, and a marginal rate of 32%. He has $4,000 in deductions from his take home pay, other than income tax. His average tax rate in retirement will be 15%. He expects that he would need enough to provide savings to fund 80% of the amount he will spend next year, once he retires. That is 80% of his spending or consumption, not 80% of his income. See the note in italics at the end of the question. He has $40,000 now in his RRSP and no other savings. He will receive Canada Pension Plan pension of $9,000 p.a., Old Age Security of $5,000 and an employer pension of $10,000, in today's dollars, all indexed, starting age 65. To make it clear, this is the real dollar value of the pensions expressed in today's dollars, which allows you to do this problem in real dollars.
He wants to provide enough to carry him to age 90.
He can save $3,000 p.a. from his salary next year and deposit it into an RRSP. This will exhaust his RRSP limit. He will deposit the tax refund into a Tax Free Savings Account.

You will recall from the mid-term exam that all income in a TFSA accumulates tax-free.

To simplify the problem, assume that each RRSP deposit is at year-end and the tax refund is also received and deposited at year-end, starting next year and ending at the end of his last year working.

a)How much is he planning to spend next year in real dollars?
(6 marks)
b)If he earns a real rate of return of 4% p.a. on his investments, by how much will
he fall short of his goal or exceed it? (14 Marks)