If you set aside $$4,000$ per year $($i$.$e$.,$ one deposit of $$4,000$ each year$)$ in a Roth IRA for the next $20$ years $($the first contribution is to be made exactly one year from now, so use an ordinary annuity setup$),$ how much will you have at your retirement in $20$ years if your IRA earns $8\%$ APR, compounded quarterly?