Alison makes $$85,000$ a year. Her employer offers her a $5\%$ match into her $401$k retirement fund $($meaning that she contributes $5\%$ of her income and her employer also contributes $5\%$ of her salary$).$ She also expects her salary to increase by $2\%$ each year $($excatly every $12$ months. In excel increase the contribution on month $1$ of each year$).$ If she contributes every month into her $401$k for the next $40$ years, and she earns $12\%$ interest, how much will Alison have in her $401$k by the time she retires?

Group of answer choices

$$928,027,000,000$

$$8,416,000$

$$9,775,000$

$$340,000$