Jodi and Paul Sprague raised their daughters with a guiding principle: understand the value of a dollar. By elementary school, Evelyn and Olivia were learning about mortgages, car insurance, and basic accounting in the carpool lane.

Early one June morning, before Evelyn, 17, and Olivia, 19, left for their summer jobs, Jodi sat them down with news that threw the Spragues’ carefully managed budget into question. The student-loan payments the family had budgeted for since 2015 were surging from $404 to $1,014 monthly, starting in September.

She and Olivia began to cry. Olivia was about to start her sophomore year at Georgia Southern University…