Question: James turns 20 today, and makes plans to start saving for his retirement now. He wishes to retire at the age of 65, and believes

James turns 20 today, and makes plans to start saving for his retirement now. He wishes to retire at the age of 65, and believes he cannot live past age 85. At retirement, James hopes to withdraw a constant monthly income, starting from his 65th birthday. He intends that his last withdrawal will take place a month before his 85th birthday. James assumes he will be able to earn an annual effective interest rate of 5% per annum on his savings. Compounding is monthly.

(a) James can set aside a monthly income of $200, starting at his 20th birthday, for 10 years. For the next 10 years, starting at his 30th birthday, he estimates that he will be able to set aside $500 monthly. Thereafter starting at his 40th birthday till just a month before his 65th birthday, a monthly amount of $750. Based on his plans, how much can he expect to withdraw each month upon retirement?

(b) If he hopes to withdraw a constant monthly amount of $5,000 during his retirement, what lump sum can he contribute or withdraw at age 30 assuming that his plans as laid out in (a) is unchanged?

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