Leonard Hofstadter would like to retire in $30$ years $(1$st withdrawal in year $31).$ He is told by Raj Koothrappali that he will need about $$230,000$ per year $($in t$=31$ dollars$)$ to fund his retirement. Leonard wants to be able to maintain that level of purchasing power for $25$ years $($Assume inflation $=2\%$ per year$).$ Leonard plans to increase his savings by $5\%$ per year and expects to earn $8\%$ per year on his investments.

What is Leonard$$s retirement number? That is$,$ how much does Leonard need to have saved by the end of year $30?$

How much does Leonard have to save the first year to fund his retirement goal?