Calculate rate by date

I have a spreadsheet that I use to calculate anticipated income. It lists clients I see by date (which I also use to track tasks required for the client). I use a formula to import data from another page which lists the rate for that client for that service. I am able to sum the column to have an idea about the income to expect as often there is a delay in payment. It works well, except a couple of times per year the rates may change. If I update the rate, the import formula changes the rates for the previous dates of service. I am looking for a solution to 1) prevent the previous entries from changing or 2)compare the date the service was provided against the date the fee changed. Ie, if the service was provided after the date in cell A1, but before the date in A2, charge the rate in B1. If it was provided on or after the date in A2, charge the rate in B2. And written so that I can keep adding dates in Column A and rates in Column B as they change. Any ideas?