Your father is about to retire, and he wants to buy an annuity that will provide him with $$40,000$ of income a year for $20$ years, with the first payment coming immediately. The going rate on such annuities is $8\%.$ How much would it cost him to buy the annuity today?

$607,905\mathrm{.}82$

$416,110\mathrm{.}34$

$486,324\mathrm{.}66$

$424,143\mathrm{.}97$

$729,486\mathrm{.}98$