Your brother works as an engineer. Today is his 24th birthday. At his birthday party,he asks for your advice on saving for his retirement. He plans to retire at 65 years oldand he expects to live for another 20 years afterwards. He wants an income of $30,000, per year during his retirement years, to be paid annually on his birthday (starting fromhis 65th birthday). He plans to save some amount at each birthday from the age 25 to64. He thinks about saving a constant amount for the first 10 years and then increaseshis saving at 3% each year until the last one before his retirement. The bank providestwo types of accounts. One account pays 6.9%/year compounded quarterly. The otheraccount pays 7%/year compounded annually.

(a) Which account would you recommend? Why?

(b) After choosing the proper account, how much should your brother save each yearfor the first 10 years?

(c) What is the balance of your brother's account right after he makes his deposit inhis saving account on his 50th birthday?

(d) In fact, your brother is not entirely sure how long he will live. Although he expectsto live until 85 years old, there is actually an equal probability that he will die at theage of 75, 85, or 95. If this is the case, would you change your answer to part (b)