I think you need to look at it from monthly -> house price and not the other way around. If your budget / purchasing power is $1000 /m then your house budget is roughly as follows:

  $190,000 @ 5% interest
  $210,000 @ 4% interest
  $235,000 @ 3% interest
  $275,000 @ 2% interest
  $310,000 @ 1% interest

[Note - not exact numbers; 30yr mortgage; mortgage calculator.org via guessing numbers until the monthly was close enough to $1k]