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Lease rate is not the same as convenience yield. You have to pay the lease rate if you do not have the commodity and want to short sell it, i.e. you have to lease it to deliver it and pay a lease rate (as if you lease a car). The convenience yield is essentially a "plug" that explains the relationship between forward and spot prices. It is interpreted as the benefit from holding the commodity physically. Because convenience yield is subtracted, it explains backwardation or contango.

You should definitely have a deeper look into the commodity section in the ORIGINAL CFAI Book. There are plenty of example and explanations.

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