An investor wants to save for retirement in $40$ years. She evaluates two plans:

Plan $1$: Invest $$6,000$ per year for $40$ years.

Plan $2$: Wait $10$ years and then invest $$9,000$ per year for $30$ years.

If the rate of retum is $5\%$ per year, which plan will give her the most for retirement? How much will she have?