I must say you do have a more unique story than most (and a username too, I might add!). @SuperMarioVT is right when he says you need to make the best decision for you where you are currently.
For the moment, let's focus on the value of an MBA for you that doesn't have to do with salary (we'll get into that later). At your age and background, if you're looking to make the shift into PE or MC, you're forced to rely on your personal network without an MBA. Which isn't impossible, just difficult. The value of an MBA is about brand and networks and that's the value for you. If you want to move into management consulting, you could really value from the degree and the structured career services. If you're looking to PE, you could find benefit in the clubs and organizations on campus to get involved in that have inroads into the local/national PE/VC scenes. In other words, if you're focused on changing careers, then yes, an MBA will help you.
Both MC and PE should, with bonuses, get you in the range of your existing salary (MC a little less, PE more). Keep in mind, schools ask you to disclose salary and certain rankings take into consideration the differential in pre-MBA/post-MBA salaries so if they do accept you, their rankings could take a slight hit in this regard. In other words, your story for "why an MBA' needs to be airtight and your value to the class articulate. Especially because you already have one grad degree.
Now - on to the rankings. Top 5 programs are going to be stretches for you. It really comes down to your age unfortunately. Some programs outright ding older applicants while others don't view them all that favorably. Without knowing your GMAT, it's difficult to say what is a stretch and what is aligned, etc. So let's bifurcate the importance of rankings:
Management Consulting: All top 20 programs feed into MC. The top 10 have greater placements into Tier 1 (MBB) firms while all have considerable placements into Tier 2 (e.g. Deloitte) firms. So if your profile makes the 10 - 20 range more a fit for you (and it might be - I don't have the necessary information to say this yet) then your doors into MC are still wide open.
Private Equity / VC: This is difficult no matter how highly ranked a program you get into. However, these programs look heavily to the top 10 and select programs in the 10 - 20 range. PE is just flat out difficult to get into without previous experience or relevant experience so let's just call a spade a spade there.
Therefore, school selection for you will be a balancing act between having the MC/PE/VC opportunities available and the fit of your profile. I think if you're looking to switch careers, we can put forward a logical and compelling story. So I'm not concerned about that. Even though your age is on the higher side and your extracurriculars are decent, I think you have a lot to offer an MBA program and I feel we can show them that. I'm not too concerned with that so, if you want to go the MBA route, it's within reach!
However - that doesn't always mean that's the right choice for you. That's up to you. I believe if you want to make the career hop into something as selective as MC or PE, you need the MBA program's network and brand.
I'm happy to talk about this in more detail with you. If you'd like - feel free to set up time to chat with me. I handle all our free consultations so it's a good way to continue this conversation offline. If you want to go through the forum, that's perfectly fine too. I want you to make the best decision for you and I'm happy to talk it through with you.
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