Time Value Of Money

1. Today is Craigs 24th birthday, and he wants to begin saving for retirement. To get started, his plan is to open a brokerage account and to put $1,000 into the account today. Craig intends to deposit $X into the account each year on his subsequent birthdays until the age of 64. In other words, Craig plans to make 40 contributions of $X. The first contribution will be made one year from now on his 25th birthday, and the 40th (and final) contribution will occur on his 64th birthday. Craig plans to retire at age 65 and he expects to live until age 85. Once he retires, Craig estimates that he will need to withdraw $100,000 from the account each year on his birthday in order to meet his expenses. (That is, Craig plans to make 20 withdrawals of $100,000 each-the first withdrawal will occur on his 65th birthday and the final one will occur on his 84th birthday.) Craig expects to earn 9 percent a year in his brokerage account. Given his plans, how much does he need to deposit into the account for each of the next 40 years, in order to reach his goal? (That is, what is $X?)

2. Carla is interested in saving for retirement. Today, on her 40th birthday, she has $100,000 in her investment account. She plans to make additional contributions on each of her subsequent birthdays. Specifically, she plans to: Contribute $10,000 per year each year during her 40s. (This will entail 9 contributions--the first will occur on her 41st birthday and the 9th on her 49th birthday.) Contribute $20,000 per year each year during her 50s. (This will entail 10 contributions--the first will occur on her 50th birthday and the 10th on her 59th birthday.) Contribute $25,000 per year thereafter until age 65. (This will entail 6 contributions--the first will occur on her 60th birthday and the 6th on her 65th birthday.) Assume that her investment account has an expected return of 11 percent per year. If she sticks to her plan, how much will Carla have in her account on her 65th birthday after her final contribution?

Note: Need detailed and conceptual notes on this question of both parts. The question carries 20 marks so, please answer accordingly. Thank you. ill upvote.