I want to retire at 32 as a software engineer, would this work?

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A hypothetical low average of 55k (after taxes) in earnings after working as a software engineer for 8 years (starting at 24) will leave me with 320k, assuming I spend 25k each year in housing, food, and drugs. This is enough money to relocate and retire for 16 years at the cost of 20k each year.
besides inflation

Other answer:

Only if you want to be poor the rest of your life and live alone in a run down trailer park.

Retiring at 32 will take some extremely good luck, and if you are that lucky, you probably wont want to retire.

Now if you are any good you can opt out of the "rat race" and work part time, short term contract jobs, travel to different places etc. But that gets old after while..

Get some useful qualifications, invest some of the money you earn, buy a modest house and affordable car, and you can afford to not work too hard and still be getting ahead.

If you intend to retire, you probably want a couple of million invested in things that earn an income. You keep the investment intact, and live off the money that you earn. Then if you live to be 105, the income keeps coming.

"Retiring for 16 years" is not a retirement, it's a sabbatical. After those 16 years you're 48 and you're still far from the retirement age. Even if you live in a country where the government funds a minimal retirement for everybody, you'll have problems.

Another computation is that the average profit rate of capital is of the order of 5%, and relatively stable on History, so if you can amass 20 times your yearly needs then you can live without working for an infinite time. It turns out that if you save about half of your salary it means you need to work about 40 years, and it's essentially the length for which most people work.

So after 16 years do you plan to return to the work force or just become a ward of society??? What you're not looking at is that at today's average life span you'd have about another 43 years to live. So what's your plan for the last 27 years or so. Housing, food, drugs, are only a part of the annual costs. Your leaving out clothing, auto, insurances, etc., etc., etc. You're also not looking at a potential massive market downturn as was experienced in 2008 where people were losing where people were losing as much as 30% of their investment portfolio. Additionally, the average interest earned on investments since the 2008 time frame has been around 5% so you need to kind of factor that in. Since you apparently will only have your cash/investments to live on since you will not qualify for any Social Security based upon your short longevity in the work force. In summary that $320k simply won't support you on it's own and you'll be tapping the principal much of the time which will drastically shorten your 16 year estimate as your interest income will perpetually be declining. My recommendation … you need to come up with a more realistic plan based upon the numbers you provided in your question.
Jake No Chat:
That is a plan, but I do think that you will need more money that that for living expenses. Unless you have other income sources, that plan would not work. Hang in there beyond 32, and seek advice of reputable financial planners. I have seen plans that suggest a person of ordinary retirement age (say 62 and beyond) would need $300K to retire, others indicated $750K, and yet others indicated $2M. It really depends on how long you will live and what your expenses will be. In any case, good luck, we all need some of that.
the "value" (the purchasing power) of the $ in 1977 was almost 4x what it is today

so the amount you could buy with your 20k in 1977 was almost 4x what you could buy with it 38 years later
(You are talking about retiring in 8 years, but are referring to spending 20k when you retire
that means you are making no allowance for inflation in those 8 years as well as any inflation after then)

Could you live on 5k today?

cos if you cant you would not be able to live on your 20k in 38 years time (when you would be 24+8+30= 62 years old)(and thats assuming "value" of the $ falls at the same rate as in the past 38 years)

For you to have the equivalent spending power in 38 years time as 20k today the amount you have to spend would need to be at least 80k, and that means you would need to have around 4x350k = 1.5 million $ saved in 8 years-
thats almost 200k/anum – or nearly 4x the income you are thinking about

last thing is- this calculation only gives you an income up t age 62

what you gonna do if you live longer and aint got any savings left?

If you are a software engineer, you need to work on your assumptions and math skills. You seem to have forgotten about inflation, and health insurance costs; and did not mention where you were going to live, and what you are going to keep yourself busy. {Some hobbies are very expensive.}
Do the math and see! If you can't figure this out, then pick another career!
Play the lotto!