I am enrolled in a Personal Finance class that is teaching me the skills I will need to be financially successful. (PROGRESSIVE PRESENT)

Is this the correct verb tense?

I am enrolled - verb?

If you call it the present progressive (in that word order), yes.

http://grammar.ccc.commnet.edu/grammar/verbs.htm#tense

and
http://grammar.ccc.commnet.edu/grammar/progressive.htm

Yes, "am enrolled" is the correct verb tense in this sentence. In this case, the verb "am" is the helping verb and "enrolled" is the main verb. The progressive present tense is constructed by using the helping verb "am" followed by the present participle of the main verb, in this case, "enrolled." This verb tense is used when actions are happening now or around the present time.