Yes, Mettle and FreeAgent share category and receipt information for transactions to make your bookkeeping easier. This means if you categorise a transaction in your Mettle app for the current tax period this should update your tax calculation.
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There are a small number of cases where categories selected in Mettle will not show in FreeAgent. In these cases you'll need to explain the transaction in FreeAgent in order to update your tax calculation. Find out more here.
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Once your accounts or tax submission have been completed in FreeAgent your tax calculation won't update.