How much money would I need if I wanted to retire at 50 and withdrawal $65k per year till I was 100

Hello this is a question based on present value (PV), future value (FV), and annuities.  

How much money would I need if I wanted to retire at 50 and withdrawal $65k per year till I was 100.  A few more details.  I am 30 years old now, the $65k would need to keep up with inflation and whatever lump sum I had at 50 years old would grow at 7% and when I die at 100, my balance should be $0.  The 65K is in today’s dollars, so it would need to be adjusted to the FV of 20 years: 65(1+.03)^20.

I was looking at using the formula for a growing annuity payment (http://www.financeformulas.net/formulaimages/Growing%20Annuity%20Payment%202.gif)  but the issue is that it doesn’t deduct from the principal lump some (I think).  Who knows, this formula could actually be all that I need and I already have my answer.  

 

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