A couple plans to retire in $25$ years. At that time, they would like to have enough money in an account so that they can receive a $$3,600$ every month end for $25$ years. The account earns APR $5\mathrm{.}4\%$ and will continue to do so until there is a zero balance in the account. To achieve this goal, how much money does the couple need to have in this account by the time they retire?

$$\_\_\_\_\_\_\_\_\_\_\_\_\_\_.($calculate to cents.$)$