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Look up rate for specific person in effect on or after a date

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In this Google Sheet, I have one sheet, "Transactions", with a rate entry that should be auto populated from a table in the "Rates" sheet. The formula should look up the rate for the listed person in effect on or after the date of the transaction.

Transactions sheet:

date      item          person   hours   rate    total----      ----          -----    -----   -----   -----1/1/21    design work   John     2       75      1502/15/21   design work   John     2       90      1803/5/21    design work   John     2       100     200

Rates sheet:

person   rate   effective date----     ----   --------------John     75     1/1/21John     90     2/1/21John     100    3/1/21Nia      125    1/1/21Nia      150    2/28/21John     120    6/1/21

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