Today, you celebrated your $25$th birthday. You just landed a new job in Firm A$.$

Firm A $($Tenure $12$ years; Age $25$ to $37)$

Firm A provides you a $401-$k plan, where you deposit $$350$ every month for $12$ years. Firm A matches your $401-$k at $80\%($matching funds are deposited annually$)$ and pays interest at $6\mathrm{.}6\%$ compounded monthly. At the end of your $12-$year tenure, you change the job to Firm B$.$

You roll$-$over your entire $401-$k to Firm B$.$

Firm B $($Tenure $20$ years; Age $37$ to $57)$

At Firm B$,$ you contribute $8\%$ of your salary to the $401-$k$.$ Deposits are made annually. Your starting salary at Firm B is $$80,000$ and you expect to earn $2\mathrm{.}5\%$ pay raise every year. Firm B matches your contribution at $50\%($matching funds are deposited annually$)$ and pays interest at $7\mathrm{.}2\%$ per year compounded monthly.

You leave Firm B on your $57$th birthday and join Firm C$.$

You do not roll over your $401-$k$.$

The account earns interest even after you end your tenure at Firm B$.$

While at Firm B$,$ on your $40$th birthday, you had a hardship withdrawal of $$50,000$ from the account.

The entire amount $($$$50,000)$ was returned to the account on your $45$th birthday.

Firm C $($Tenure $9$ years; Age $57$ to $66)$

At Firm C$,$ you contribute $$900$ every month to your $401-$k$.$ The firm matches at $70\%$ and deposits the money monthly. The account pays interest at $6\%$ compounded monthly. On your $66$th birthday you resign from Firm C$,$ and retire from workforce. You leave the money in the account., and it continues to earn interest.

Where are you? $($For $6$ years from age $66$ to $72)$

Retired, enjoying somewhere. No info given. Not needed for the problem.

French Riviera $($age $72$ to $85$ and beyond$)$

On your $72$nd birthday, you move to French Riviera to have a luxurious lifestyle.

You consolidate your accounts by rolling$-$over your $401-$k balances from Firm B and Firm C to a new retirement account at Fidelity Investments. The account pays $5\mathrm{.}4\%$ compounded monthly. You start withdrawing $$35,000$ every month needed for your luxurious lifestyle.

Answer the following questions.

What is the account balance in the $401-$k account at Firm$-$A at age $37?$

What is the account balance in the $401-$k Account at Firm B at age $57?$

What is the account balance in the $401-$k Account at Firm B at age $65?$

What is the account balance in the $401-$k Account at Firm B at age $72?$

What is the account balance in the $401-$k Account at Firm C at age $66?$

What is the account balance in the $401-$k Account at Firm C at age $72?$

What is the balance in the Fidelity Retirement Account at age $72($soon after consolidating the accounts$)?$

What is the balance in the Fidelity Retirement Account at age $85($assuming the monthly withdrawal are low enough to result in a positive balance at age $85)?$

OR

When will you run out of the money if $$35,000$ withdrawals are too much do result in a positive account balance at age $85?$