You are planning to save for retirement over the next $20$ years. You currently have $$500,000$ in an account earning $4\mathrm{.}5\%$ compounded quarterly. In addition, you will invest $$650$ per month in a stock account and $$350$ per month in a bond account. The return on the stock account is expected to be $7\%$ per year and the bond account will earn $4\%$ per year. When you retire you will combine your money into another account which will earn an expected $3\%$ annually. When you retire, how much can you withdraw each month from your account assuming a $20-$year withdrawal period.