You intend to work for 30 years before you retire and will save for your retirement during that period with fixed monthly payments invested in the S&P 500 index at the end of each month. During the first 10 years of retirement, you would like to withdraw $5,000 at the end of each month, and during the next 10 years of retirement, you would like to withdraw $6,000 at the end of each month to offset the effects of inflation. How much do you need to save each month if the expected rate of return on the S&P 500 is 8%? Please show clear steps.