When does the duality functor commute with the wedge power functor?

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When working with modules over a fixed commutative ring, I know that $(M \otimes N)^* \cong M^* \otimes N^*$ provided either $M$ or $N$ is finitely generated projective. Does it follow that

$(\bigwedge^l M)^* \cong \bigwedge^l M^*$

whenever $M$ is finitely generated projective? Also, does anyone happen to have a textbook source for this fact (if it is true)? I've been using Aluffi's algebra text as my go-to reference, but I couldn't find this mentioned anywhere in the book.