Trying To Use TimeLine to calculate values for different time periods

I have an excel table that records the Weekly fees that are due from residents. The fee is valid for a specific time period and changes throughout the year.
I am looking for a way to calculate the total fee due during a month (bearing in mind that the month could have different fee rates, the fee rate is Weekly, and the total fee is actually comprised of three different values)

I have a table called 'FundingTable' in the 'Funding Information' Worksheet. This contains the raw data for fees and the date ranges that they are valid for ('Start Date' and 'Change Date')
When the person leaves the 'Discharged Date' will have a date and obviously no fees are due after that day.

I am trying to get a pivot table with a timeline in 'Monthly Income' worksheet that will sum the income for the month, but I can't work out how to factor the different rates that could be in effect over the month...? Ideally I would like the pivot table to show the totals due from each 'Funding Source' in 'Funding Table'..

I hope this makes sense, cos my brain is fried! lol

thanks in advance?

Hello MichealP1 and Welcome to Excel Forum.
I am not sure that this could be done using a pivot table.
If you could provide us a manual example of how August should look, since Abraham Lincoln's rate changes mid-month, then someone may be able to come up with a proposed solution using some type of Excel functionality.
Let us know if you have any questions.