Liz is currently age $43$ and happily divorced. She is concerned about becoming a burden on her children and would like some advice regarding saving for retirement. Liz estimates based on her current expenses, that she would need $$60,000$ per year in income and that Social Security will provide $$23,000$ in today's dollars at her full retirement age of $67.$ Liz would like to retire at age $67$ and plan for a life expectancy of $20$ years. She estimates that inflation will be $3\%$ and that she will earn $8\%$ on investments prior to retirement and will earn $6\%$ on investments during retirement. What amount does Liz need to save at the end of each year in order to reach her retirement goal if she currently has $$110,000$ in her $401(k)?$

a$.$ $$6,427$

b$.$ $$6,941$

c$.$ $$14,575$

d$.$ $$15,741$