You just turned $30$ years old and you are looking to save for retirement. You are planning on

making yearly deposits starting next year for the next $35$ years $($a total of $35$ annual deposits with the first deposit

occurring on your $31$st birthday and the last deposit on your $65$th birthday$).$ One year after you make your last deposit,

you will begin making withdrawals to fund your living expenses. Since your current yearly expenses are $$65,000,$ you

expect that you will need $$65,000$ per year in real terms when you retire. You plan to withdraw funds over $25$ years

$($the first withdrawal you will make will be as of your $66$th birthday and last withdrawal will be on your $90$th birthday

for a total of $25$ withdrawals$).$ After the last withdrawal, you want to have $$500,000$ in today$$s terms $($real terms$)$ left

over in your retirement account. The interest rate in nominal terms is $8\mathrm{.}50\%$ and the inflation rate is $3\mathrm{.}75\%.$