Joel and Rachel are both retired. Married for $45$ years, they've amassed an estate worth $$11\mathrm{.}4$ million. The couple has no trusts or other types of tax$-$sheltered assets. If Joel or Rachel dies in $2021,$ how much federal estate tax would the surviving spouse have to pay, assuming that the estate is taxed at the $40$ percent rate?

Note: Leave no cells blank $-$ be certain to enter $"0"$ wherever required.

Federal estate tax