Sophia is $45$ years old and aims to retire in $25$ years. With a family history of living into their early $80$ s $,$ she estimates a retirement age of $80.$ Sophia's current salary is $$150,000,$ and she anticipates needing $70\%$ of this amount annually in retirement. She expects a return of $5\%$ on her investments and an inflation rate of $4\%.$ Sophia currently has $$500,000$ saved for her retirement. Her Social Security benefit at full retirement age of $67$ is estimated to be $$20,000$ per year in today's dollars. Using the annuity method, how much does Sophia need to save each year at year end to meet her retirement needs?

$$15,268$

$$8,056$

$$10,017$

$$12,894$