Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current annual salary is $50,000, and you expect your salary to increase at a rate of 2 percent annually as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be a constant percentage of this year's salary. Likewise, you expect to deposit a constant percentage of your salary each year until you reach age 65. Assume that the interest rate is 7 percent. [6 marks]

1. a) You expect to have $200,000 in your retirement account at your retirement (age 65). What percentage of your salary must you save each year?

2. b) Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current annual salary is $50,000, and you expect your salary to remain constant for the entire work period. Your brother promises to save $5,000 every year from your 31st birthday until your 65th birthday (the first deposit is made on your 31st birthday). On your 65th birthday, he will give the savings to you as a birthday gift. To save for your retirement, you also plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be a 10 percent of this year's salary. Likewise, you expect to deposit a 10 percent of your salary each year until you reach age 65. Assume that the interest rate is 7 percent. On your 65th birthday, how much do you have if you receive the gift from your brother and withdraw all the savings from your retirement account?