Tableau Weighted Average of Last Value in Date Group over Running Sum Across Extra Level of Detail not in Report - tableau-api

Question

I am an absolute Tableau beginner, so forgive my lack of proper terminology.
Context
To give some context to the problem, think of the dataset as the balances and current interest rates of two different loans for which we are trying to calculate a weighted average cost of funds at any point in time, while retaining the ability to filter on Program (specific loan).
I have a single dataset that looks like:
The Balance field is used as a running sum, i.e. to get the actual balance as of 4/30/2022, you would sum the column across all Date values on or before 4/30/2022.
The Rate field is the opposite: it represents the discrete interest rate as of the Date. Thus, it cannot be summed.
Each data point is specific to a specific loan, or Program.
So to get the interest rate of Program A as of 4/30/2022, you would simply grab the Rate value of the row where Date = 4/30/2022 and Program = A, or 5.30%. Sums are fine here, since the value of Rate is never repeated for a single Program and Date combo, but we cannot use a running sum.
On the other hand, to get the balance of Program A as of 4/30/2022, you would need to add (running sum) the Balance values for all rows where Date <= 4/30/2022 and Program = A, or 10,000 + -2500 + -2500 + -2500 = 2500.
Problem / Need
I need a report (or whatever it's called in Tableau) with the following:
Date as a column
Measures as rows
This report would NOT include Program as a row or column, but would include it as a filter.
In this report, I need a Weighted Average Cost of Funds measure.
This is effectively the weighted average Rate over/weighted by the running sum of Balance across Programs included in the filter, of course for any given Date in the columns.
In other words, by Date, latest Ratefor eachProgramtimes thePrograms running sum of Balance, divided by running sum of all Balancesfor allProgram`s included in filter.
Here's an example in Excel:
Here's an example if we were to exclude Program A:
And here's an example if we were to exclude Program B:
Finally, here's the formulas underneath everything in the Excel example: