Viewing a single comment thread. View all comments

hmiamid OP t1_irg4ih8 wrote

Reply to comment by pookiedookie232 in [OC] House price you can afford by paying 1000/month for 30 years vs. interest rate by hmiamid

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.

9

pookiedookie232 t1_irgbp70 wrote

Been a lot of years since I did real math so I probably won't go calculate this, but even if the function never reaches zero, anything under half a cent I think we could say rounds to zero and would put your max house price at $0.

3

ajour7 t1_irgdhzj wrote

If your house price is $0 then you cannot accrue interest so you cannot logically have a payment of $1000 (or any amount really)

3

pookiedookie232 t1_irgevm1 wrote

Yep, once I looked at the formula I was like, "Doh!" Can never actually be zero. But it could be less than half a cent, which is essentially zero due to rounding in financial systems. I calculated that 240,480,000% interest will net a $1,000 payment for 360 months on a .499 cent loan.

3

ajour7 t1_irgdqto wrote

Btw, Great visualization OP!! This is something very useful for anyone who has bought or has aspirations for buying a home.

1

pookiedookie232 t1_irge9pi wrote

Okay, so I ended up using excel, and found that around 240,480,000% interest the max loan is .499 cents, so essentially zero, lol. You pay $1,000 per month for 30 years on essentially nothing!

1

pivantun t1_irgeift wrote

That doesn't sound right for a standard 30-year-fixed-rate loan. They are designed to fully pay-off the principal at 30 years.

1

hmiamid OP t1_irgksfl wrote

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.

3

pivantun t1_irglrby wrote

Oh, I think I understand what you're saying. That as the interest rate goes up and you limit the monthly payment to $1000 then you'll have a situation where the loan would not get paid-off. I don't think that's realistic, since the home would be repossessed if you didn't make the correct payment.

My point is that a standard 30-year loan could, in theory, have any interest rate, but it would still be paid off in 30 years. You just may have a payment that's more than $1000/month.

1