You would like to retire at age 65. After consulting an actuarial table, you believe that you will likely live for 30 years in retirement. You estimate that you will require $7,000 per month in living expenses in retirement which you will begin to withdraw immediately upon retirement. Additionally, you would like to leave $1,000,000 to your heirs upon your death. To provide for this retirement, you will begin saving money at the end of each month upon your graduation. Assume that you will graduate on your 22nd birthday so that you have a full 43 years to save for retirement.
While working, you will be able to earn a 12% return on your investment, but upon retiring, you will switch to a safer investment that only provides a 6% return.
How much must you save each month while working to fund the retirement you desire?