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Please explain to me, why do we need 'of' in the sentence below. What would happen if we omitted the 'of'; would it change the meaning of the sentence?

This conclusion is of more than academic interest to me since my wife asked me to suggest how we should invest funds from a rolled over CD for a college fund.
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This is the idiom and you can't eliminate the "of." In translation, it says:

This conclusion is of more interest than just academic interest to me since my wife asked me to suggest how we should invest funds from a rolled over CD for a college fund.

It could be rephrased again as:

This conclusion has/presents more interest than just academic interest to me since my wife asked me to suggest how we should invest funds from a rolled over CD for a college fund.

Something is of interest (idiom),
not
something is interest

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The of is required.

See "be of"

CJ
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