Question

Is the use of pronouns correct in this sentence or should their be his/her?

1. Most importantly, a person should track their expenses and make purchases that are going to be assets for them in the long run.

Answer 1

Since the pronouns refer to "a person," the pronouns also need to be singular.

. . . should track his or her expenses . . . be assets for him or her in the long run.

A much better way to word this sentence is to make "person" plural >> "Most importantly, people should . . ."

Using a plural antecedent would make your sentence correct -- their expenses . . . for them . . .