Professor Slezak wants to start saving for his retirement, which will start in 15 years. He currently has no savings since he has been enjoying life and had to put two daughters through college (at out-of-state universities). He expects to live for 20 years after he retires (based on a forecast of longevity given his family's medical history and trends in medical advances). He would like to have $10,000 per month and retire to a $1,000,000 home in the Pacific Northwest of the United States. Assume he can get an effective annual rate of 5% (r = 0.05) while he is savings, but will want his savings to be safe, only earning an effective annual rate of 2% (r = 0.02) during retirement.
How much does Slezak need to save per month over the next 15 years?