Julia, who is $22$ years old, is planning for retirement. She anticipates her living expenses the first year of her retirement at age $70$ to be $$300,000$ and to increase by $4\%$ each year from that point forward. She believes she will live to age $90.$

How much should she have in her retirement fund by age $70$ if she plans to keep the assets invested and anticipates a $6\%$ investment return?

Round your answer to the nearest thousand and do not use commas or dollar signs $($ex: $$236,958$ should be entered as $237000)$