At $20$ years old, Josh is an avid saver. He wants to put an equal amount each year from age $21$ to $50(30$ years$)$ such that starting at age $65$ he can make a guaranteed annual withdrawal of $$40,000$ forever without touching the corpus, which will be the inheritance money for his family. He will make no deposits during the years of age $51$ through $65.$ At a conservative return of $5\mathrm{.}5\%$ per year for all the years, what amount must he invest each year from age $21$ through $50?$

The amount that must be invested each year is $ $(2.$