You have $35$ years until your retirement. You currently have $$50,000$ in your $401($k$)$ account. You can contribute $$10$ thousand per year and your company will match $50$ percent of your contribution. You expect an average return of $8\%$ over the life of your $401($k$)$ investments.

a$.$ What is your future value of your $401($k$)$ in $35$ years?

b$.$ What is your future value of your $401($k$)$ if the average return drops to $5\%?$

$351,950$

c$.$ Given the original information above $(35$ years until retirement, average return of $8\%,$ and $$50,000$ currently in your $401($k$)),$ how much would you have to start saving per year if you wanted your $401($k$)$s future value to be $$1,500,000$ by the time you want to retire?