1. you don't really expect the market to crash the day after the interest rates rise. Its a slow progress.
2. how do you think UK banks calculate people's affordability then?

The point is how fast the curve drops from low mortgage rates to high ones. This in turn drives the house prices down because of lower purchasing power. And that's for everyone. It won't be half though because every buyer is not a new buyer. Remortgaging is in some countries (like the UK) a necessity too as they are mostly 5 yr fixed then go to SVR. Of course if you lock a 30yr low rate, you don't care about all this. But it's not the case of everyone and some countries will be more affected than others.

It's an arbitrary unit. Multiply by what you like. 2000/month means you multiply the y axis by 2.

If you go and apply for a mortgage on a new house, they look at your current income. Maybe you'll be able to pay more later but it's not the point here. If rates rise from 1% to 7%, and you got the OK from the broker for a 311k mortgage a few months ago, now you can only be accepted for an 150k ish one.

Which happened in 2008 with adjustable rate mortgages. In the UK, practically every mortgage is variable rate.

Or save money by stopping eating avocado toasts.

In terms of abstract maths, it's called a limit towards infinity. We can never realistically create an infinite interest rate, but if we do, we pay 1000/month to own nothing after 30 years (or any amount of time for that matter). The principal is simply 0. I mean the original question I think was more of a mathematical curiosity than anything realistic.

Sorry, I am not familiar with property taxes. I'm not in the US. But it looks like it's variable in time and place. And it's not compounded and wouldn't change with interest rate (at least not directly).

Sure. Formula is (1-q^-N )/(q^(1/12)-1) where q is 1+r, r is the interest rate and N is the mortgage term in years. Make sure to put r without a percentage. So f.ex. for 5%, r = 0.05 and therefore q = 1.05. The 1/12 is because we pay every month.

Yep. Warren Buffet said interest rate is like gravity. It brings price to a more "down to earth" value. Low interest rates makes prices "float" too high.

It's not a logarithm. Formula is (1-q^-N )/(q^(1/12)-1) where q is 1+r, r is the interest rate and N is the mortgage term in years.

That's why the house prices in the 70-80s (around that time) were so low. We were actually better off a few years ago than in the past if we're looking at total mortgage payments in terms of years of median income.

Yes also feel free to multiply by the amount you want. If you're thinking 2000/month just double the y axis. Relation between house price and monthly payment is proportional.

Interesting (no pun intended). I suppose we pay more downpayment at a high interest rate. Can we actually afford to save more in a high interest rate environment to prepare for a downpayment?

Good question, I don't think it ever does. As interest rate goes to infinity, you basically never pay back your capital, so you will never own any house. The curve tends towards y = 0.

So sorry about that. I played a bit with the numbers and forgot to change. I put the original parameters. So yes. It goes down a lot more.

There you go up to 20%.

https://i.imgur.com/pm5JO7A.png

Data source is only maths. Compound interest formula. Tool used is LibreOffice Calc.

This data shows what house price you can afford for a given interest rate supposing you pay 1000/month for 30 years on the mortgage.

So the idea here is, people on average when they start a mortgage, always pay a given amount per month to their mortgage (usually a third of their income f.ex.). And this is the same whether the interest rate is low or high.

For the demand to meet the offer (1000/month example), the price of houses fall. I wouldn't generally say that drastically like in this graph but this is the trend.

From 1% to 7%, the price is practically halved.

Edit: 7% instead of 6%.

Edit: a few pointed out that 1000/month isn't really how much most people pay. It is an arbitrary unit. If you are considering 2000/month, just double the y axis. Relation between house price and monthly payment is proportional.