Amount of Insurance Needed.$$Marty and Mary have jobs and contribute to the household expenses according to their income. Marty contributes$75\%$ of the expenses and Mary contributes$25\%.$ Currently, their household expenses are $ $36$ comma $400$ annually. Marty and Mary have three children. The youngest child is$12,$ so they would like to ensure that they could maintain their current standard of living for at least the next eight years. They feel that the insurance proceeds could be invested at $7\%.$ In addition to covering the annual$$ expenses, they would like to make sure that each of their children has $ $30$ comma $332$ available for college. If Marty were to$$ die, Mary would go back to school$$ part$-$time to upgrade her training as a nurse. This would cost $$$$27$ comma $188.$ They have a mortgage on their home with a balance of $$$$59$ comma $511.$ How much life insurance should they purchase for$$ Mary?

The amount of life insurance they should purchase for Mary is $?$