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

I have one sheet with transactions that I want to look like this, with rate auto populated from the other table below:

date      item          person   hours   rate    total
----      ----          -----    -----   -----   -----
1/1/21    design work   John     2       75      150
2/15/21   design work   John     2       90      180
3/5/21    design work   John     2       100     200

I want to make a rate table like this that will be used to populate the transaction table above:

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

The rate used should be the rate in effect on or after the date of the transaction. The names can be grouped if they have to be, and the dates can be sorted if needed, but it would be nice if they didn’t have to be.

Thanks for the help on this…