How many cabinet departments are there currently that report to the president

There are 15 executive departments.

Explanation:

the Secretaries of Agriculture, Commerce, Defense, Education, Energy, Health and Human Services, Homeland Security, Housing and Urban Development, Interior, Labor, State, Transportation, Treasury, and Veterans Affairs, and the Attorney General.

monarchy doesn’t have to have the hereditary element. there have been elective monarchies in the past where you choose your king-for-life and when he dies elect someone else for the job.