You would like to retire in 30 years. In addition to the pension and Social Security income you expect to receive in retirement you would like your savings to be sufficient to provide the same buying power as an amount of $1,000,000 could provide today. You anticipate that inflation will cause prices to increase by 3% per year over the next 30 years, and that your investments will earn an 8% annual effective rate of return.

You are able to save $1,000 at the end of each month in the first year, and you plan to increase your deposits each year by a constant percentage. If your estimates of 3% annual inflation and an 8% rate of return on your investments are accurate, what percentage annual increase in your savings rate will allow you to reach your goal?