You are trying to decide how much to save for retirement. Assume you plan to save $5000 per year with the first investment made 1 year from now. You think you can earn 10% per year on your investments and you plan to retire in 43 years, immediately after making your last $5000 investment.

a. How much will you have in your retirement account on the day you retire?

b. If, instead of investing $5000 per year, you wanted to make one lump-sum investment today for your retirement that will result in the same retirement saving, how much would that lump sum need to be?

c. If you hope to live for 20 years in retirement, how much can you withdraw every year in retirement (starting one year after retirement) so that you will just exhaust your savings with the twentieth withdrawal (assume your savings will continue to earn 10% in retirement)?

d. If, instead, you decide to withdraw $300,000 per year in retirement (again with the first withdrawal one year after retiring), how many years will it take until you exhaust your savings?

e. Assuming the most you can afford to save is $1000 per year, but you want to retire with $1 million in your investment account, how high of a return do you need to earn on your investments?