I am intending to purposefully try to fail a course to stay an extra semester, so I can finalize some research projects which can't be finalized otherwise. My current GPA is 3.82. How badly would that be reflected on my master's admission?
Explore all other options first. Seriously. Talk to professors whom you think to possess some common sense (especially your adviser and the department head if they are among them) explaining clearly what your situation is and what your objectives are and ask for the advice on how to proceed. Resort to the F option only if you see that there is no other way.
As to "masters admission", it depends. If you want to master in math., say, and your F is in "underwater basketweaving" or something else like that, I personally would not even notice, but if you fail algebra, that will be quite a red flag and your explanations that "it was intentional", etc. won't fly with me (also, are you going to include these explanations into your application letter or what?). So, if you follow this line, at the very least be sure to choose a subject people in the field you want to specialize in view with contempt.
In short, don't take the F.
I'm making an assumption here, but it sounds like this would delay starting your masters in favor of finishing some undergraduate research. I can't think of any scenario where someone would look favorably on prioritizing undergraduate research over graduate research. Even if your undergraduate research is amazing most are going to assume that there was really a graduate student pulling most of the weight and you were along for the ride.
Another consideration is that more and more admissions boards are using algorithms to first filter candidates. Something like an F or a minimum GPA requirement might eliminate you before someone even looks at your application.
I'm also a bit curious about your timing. You are asking this in December. Your masters program probably begins next September. That seems like plenty of time to complete an undergraduate level research project that I assume you are already well into. Taking an F now to buy yourself maybe 20-30% more time seems like way too much risk.
If you really want to stay and continue your research, talk to your adviser about getting hired as an employee. After you've earned your degree, this is really very appropriate. My adviser did this all the time while I was in grad school.
This is a seriously terrible idea that could tank your plans for a masters. As others have suggested, pretty nearly any other option might be preferable, including negotiating an incomplete or a withdrawal in that class, dumping your research project or petitioning to go an extra semester to finish it. Anything but a deliberate F. That's just dumb. There has to be a better option. Talk to your academic advisor.
Don't overestimate the importance of finalising these projects. Of course, it would be ideal to complete your undergraduate research, but it isn't worth doing it by deliberately failing a course. If the projects are valuable to your current supervisor or institution, then they will find a way for you to complete them. If they aren't valuable to your supervisor or institution, then they aren't essential for you to complete.
Having complete research from your undergraduate degree is by no means essential for Masters admission. A low GPA could see you being automatically filtered out of admissions, whereas an incomplete research project is just a good opportunity for you to explain how you would like to complete it.
TL;DR: this is a classic question of short term versus long term thinking.
Others have given good answers to your question at the practical level, so I won’t bother repeating that advice. Instead I will address your situation at a higher, more conceptual level. What you are thinking of doing is a strong example of short term thinking: that is, perceiving one course of action as preferable to another because it confers short term advantages - the savings in rent from living in the dorms apparently, or other things you have not explained - while not giving sufficient attention* to long term disadvantages of the same action and the overall advantages of the alternative course of action when those long term effects are properly accounted for.
Yes, I know you are concerned about the effect of the F on your master’s admissions, which is a longer term effect. But have you really considered all other effects? The F grade will appear permanently on your transcript. You will have to explain its meaning, over and over again, whenever and wherever you go, for grad school applications, job applications and who knows what else (hopefully your future boyfriend/girlfriend/fiancé/fiancée won’t care!). Some of the people you explain it to will believe your explanation, others will not. Some of those who believe it will find it satisfactory, others will not, and may even find your behavior dishonest and manipulative. You have no way of accurately predicting the future consequences of this intentional F grade, however much you would like to get an authoritative answer “no, it will not affect your master’s application” or “it will definitely be a problem”. All that we can be certain of is that you will be intentionally putting yourself at a potentially significant long term disadvantage, when your stated motivation to save money is short term in nature.
I don’t mean to suggest that the money and other short term advantages aren’t important; obviously they are. However, I urge you to do some studying on the nature of short term versus long term decision making and the pitfalls of concentrating too much either on the short term or on the long term. This is a well known subject and google should easily lead you to some interesting articles on the subject, which I hope will inform your thinking towards making a good decision. Good luck!
* as I think the universal disapproval of your idea in the other answers and comments rather convincingly shows.
We got a saying around here which loosely translates to the following:
Every year you delay entering the workforce costs you at least 10,000 bucks in the long run.
And that's a low number in my region. Basically, you'll work more years, start working on your pension earlier, etc.
I'm not a big fan of loans, but if you need one to survive half a year of housing, you can make it work. In the long run, you pay off the interest and the extra cost just by starting on time.
Since you mentioned it's quite an important subject and your overall high score otherwise, a loan is in the long run the cheaper and more professional option. Failing this test on purpose may bite you for the first years of employment, years which happen to go a lot easier if your marks are exemplary.
Clarification: the 10,000 bucks mentioned should be, translated to modern times and USD, at least 5 times more. Since the OP did not specify a region, I did not presume one and simply stated it for my region roughly 20 years ago. I was trying to say you're losing a great amount of money by every year you start later, regardless of the actual value. It's guaranteed more than the additional housing cost.
My understanding is that you are intending to do this because of your university offers dormitory accommodations to students at very affordable rates. I strongly advise you to just get a roommate and possibly a part time job to cover any possible cost differences.
A few years from now, the money you save will seem trivial to you and your transcripts (for which you have paid tuition and time) will be forever impacted.
This entirely depends on where you are and what are the policies of your school. If you were at a US institution, I’d tell you “no way,” since the consequences of failing a class, particularly in your next-to-last or last semester, are potentially severe.
On the other hand, if you were at a German university where the system allows you multiple attempts to pass, with the failed grades not recorded, I’d still advise against purposefully failing, but I could see the logic behind it much more clearly.
(This is based purely on personal opinion, so may not apply to others.)
If I was looking at graduate applications, I would not only be concerned with whether a potential student has a strong enough academic background, but also whether they are displaying other characteristics needed to succeed. On some of these, I think your proposed action would send ambiguous/negative signals.
- Motivation: Is your interest really in doing the research, or is it in getting cheap rent?
- Timekeeping/forward-planning: You knew the time you had available when you started your research project. While it is not always possible to predict how long research will take, were there any points where you could have adapted your aims to fit within the available time? A masters program also requires a project to be completed within a fixed time frame.
- Financial planning: You may think it's unreasonable for academic admissions to be influenced by non-academic issues, but the university needs to know you can reasonably expect to be in a position to completed your course. Are you going to run out of funds part way through? For me this wouldn't be a major decision factor in itself, but it might colour my judgement when comparing candidates who are equally academically qualified.
- Integrity: I would consider arguing that this is the most important quality needed to be an academic. Can you be trusted to carry out and report your research accurately, even if it isn't in your personal best interest?