What is the "breakeven" annual rent such that you would buy it if the rent exceeds this amount?

The interest is mentioned so you can calculate opportunity cost, the question supposes you have $200k that you could either earn 2% interest on, or buy an apartment with.

$200k x .02 = $4,000 that you can get in interest if you don't buy the apartment.

It's after tax, so nothing else to do for that component, the only remaining bit is to adjust property tax since it is tax deductible, then add up the 3 items to $6,700.

That depends heavily on what the individual's savings and projected cash flow look like. And on how important it is to them to be able to modify the space to their needs without having to justify it to a landlord. And how certain you are that you are going to stay in that location for a reasonable number of years. And on how quickly you think you could sell the house at a reasonable price, if that did become necessary. And probably other factors.

I don't think there is a simple way to answer this other than to go through your own numbers and confidence levels and decide how much you are willing to commit and how much risk you are willing to tolerate.

I rented until age 40 or so. For the early part of that, it was because I was someplace that I didn't plan to sink roots. For the latter portion, it was because I knew exactly where I wanted to be and it was waiting both for the right property to become available and for myself to be emotionally ready to make that commitment. One advantage of waiting was that since I had been saving in the meantime, I was able to decide exactly what percentage of the purchase price I wanted to borrow, and plan a payment and pay-off date that I was comfortable with. And unless somebody offers me an entirely unreasonable amount, I will not be selling before my death; I bought with the intent of aging in place.

Somebody else's concerns and trade offs may be entirely different.

By the way, a single family residence you are living in is generally not an investment; it is a cost. After adjusting for inflation, you are unlikely to get more when you sell it then you put into it in purchase and maintenance and improvements. There are sometimes exceptions, in specific markets at specific times, but you should assume that your residence will not produce a profit unless you put a heck of a lot of sweat equity into it and have the skills and budget to do that right. Buying a two family and renting out the other half is a different kettle of worms; there, you are also running a rental business which, hopefully, makes enough profit to justify the hassles.

If you continue to rent, you'll pay the rent amount, but offset it by $4,000 per year (by investing the $200k you'd have spent to buy it at 2% return).

If you buy the apartment, you'll pay $1500 in maintenance, and $2000 in taxes, but 40% of that ($800) is tax-deductible, for an actual cost of $2700.

If the rent exceeds $6700, the net cost of renting apartment exceeds $2700, making buying more cost-effective.

Unfortunately there is no formula that can help you make this determination. Aside from the basic calculations of upkeep, interest rates, taxes, etc., there are a few considerations that are often overlooked when evaluating the finances of renting vs. buying.

1. Forced investment. When you buy a home, your mortgage payment is required on a monthly basis. Part of that payment goes to principal, which is essentially an investment into an appreciating asset. Many people are either too undisciplined to make this sort of regular investment while they are renting, or they merely don't think to do so.

2. Illiquid investment. When you have equity in a home, it is largely illiquid. This helps protect home owners from touching this piece of their nest egg in a way that cash investments do not. Obviously this is not fool proof as there are HELOCs and other tools that people can use to tap into their equity, but generally it provides more friction than other investments.

3. Leveraged investment. This is the one that was not obvious to me until after I bought a home, but can make a huge difference. Most ordinary people do not invest on margin in their cash accounts. A home is a rare exception to this, where people end up investing on margin at around 5x-20x the principal. This comes with some risk (e.g. the 2008 housing crisis), but when you are comparing the opportunity cost of buying a house vs renting and putting that money into the stock market, you need to consider the fact that a house down payment is actually a leveraged investment. Let me draw an example to show how this could impact your financial outcomes.

If you bought your $200k home with a 20% down payment, that would be $40k down. Let's pretend that housing costs will appreciate 5% while the stock market appreciates 10%. After 1 year, the $40k in the stock market would be worth $44k for a return of $4k. Your home would be worth $210k, putting your home equity at $50k. Despite growing at only half the rate, the money you put into your home has actually netted you 2.5x what you would have gotten from the stock market. This is completely ignoring any additional equity you may have received from your mortgage payments.

This is a very simplistic picture of some of the financial considerations of home ownership, but I think that these considerations are often overlooked by people who are attempting to maximize their housing finances.