Toby died on $29$ March $2023.$ His death estate was valued at $800,000,$ which included his private residence valued at $400,000,$ which has an outstanding interest only mortgage of $100,000$ remaining on it$.$ Toby left his estate to his son, as his wife had died in $2018.$ Toby's wife had previously shared the private residence with Toby. What amount of residence nil rate band will be available on Toby's death estate?

$400,000$

$350,000$

$175,000$

$300,000$