Yes, they are extremely competitive----they’re offered to ~1% of the entire applicant pool. but it’s definitely worth applying as you’re already paying the application fee lol. Vanderbilt does have a strong FA program (Opportunity Vanderbilt) that meets full need (as the university calculates it) without loans. However, NPC calculators tend to break down for unusual financial circumstances (non-custodial parents, business owners, international students etc,) so keep in mind that they are ESTIMATES, not guarantees of aid.
@thumper1 is familiar with financial aid applications and would likely be able to provide some advice.