Time sheet, rates, date dependent

I am trying to figure out the best database design for the following;

I have individuals (stored in Agents table) that enter their billing or time worked each day for different projects. Now we have different rates that we pay based on the person and what the project is. And we also have to account for individuals getting pay cuts or raises over time. So....

I have the following tables;
Agents - table of each person
Projects - table of all projects we work
Rates - table with AgentID, ProjectID, StartDate, EndDate, Rate
Billing - table with Date, AgentID, ProjectID

So my current implementation a billing entry must be made by an agent, and I have to create a join to the rates table based on AgentID, ProjectID, and Date between StartDate and EndDate. This just seems incredibly ugly and all the billing data can be easily changed if a change were made to the rates. I'm assuming most time sheets calculate the total rate and store it in the table so it never changes unless someone specifically goes back to update the data? I'm just wondering if there is a better method for tracking this sort of data. Thanks