Steve is planning for his retirement. He is currently $40$ and plans to retire in $27$ years, at age $67.$ He expects then to live an additional $33$ years, until age $100.$ He expects inflation to average $4\%$ per year. Based on his assumptions about inflation and Social Security, and his desired Wage Replacement Ratio, he believes he will need $$120,000$ per year to withdraw from his retirement fund $($in nominal dollars$)$ in the first year of his retirement. He believes he can earn a nominal return on his retirement investments of $7\%$ per year before and after retirement. Assume withdrawals during retirement are at the beginning of each year.

How much does he need to accumulate by retirement?