Retirement Planning. Tilly would like to invest $$2,300$ in before$-$tax income each year in a retirement account or in

stock investments outside the retirement account. Tilly likes the stock investments outside the retirement account

because they provide her with more flexibility and a potentially higher return. Tilly would like to retire in $35$ years. If she

invests money in the retirement account, she can earn $6\%$ annually. If she invests in stock outside the account, she

can earn $8\%$ annually. Tilly is in the $24\%$ marginal tax bracket.

a$.$ If Tilly invests all her money in the retirement account and withdraws all her income when she retires, what is her

income after taxes?

b$.$ If Tilly invests all her money in stocks outside the account, what are her savings at retirement? $($Hint$.$ Remember

that the income is taxed prior to investment.$)$

c$.$ Assuming a capital gains tax rate of $15\%,$ what is the after$-$tax value of the stock investments?

d$.$ Should Tilly invest her money in the retirement account or in stocks outside the account?