You could create a new table with fields for Dept and Year; after the year has concluded, summarize into this table: have a script to go to the summary table, find the set of records for that year and Replace Field Contents with
Sum ( Paychecks_forSummary_byDeptAndYear::Amount_pay )
or use an equivalent SQL query to save on TOs and calc fields, e.g. Year ( Date_payroll )
then create a new set of fields for the new year.
If you want to see the latest comparison, you won't have to re-calculate the previous year's figures (since they won't change anymore), only the current one's.
Then your dashboard'd consist of one portal into a Cartesian relationship to Dept, and two portals into the Summary table, filtered by year and sorted by Dept.
As you may have guessed, that's only one of several different approaches, but it strikes me as the neatest one; especially since you can use that Summary table for other purposes.