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In Google Sheets: How to check if a Date is within the Date range of two other cells

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I have a sheet where column A shows one month per row and column B is supposed to calculate an amount in USD for that month.

What I am trying to achieve is that the USD values in column B are automatically calculated by looking at start and end dates specified in two other columns and then taking a corresponding value from a column next to the date range if the month in column A falls in between that range.

This is tricky to explain so I have created a demo which you can look at here: https://docs.google.com/spreadsheets/d/1vJkkEkNdLBIH6ifx_B7FJLiL9azJHyIuSRy90IRfPp4/edit?usp=sharing

I have found a few suggestions for similar problems online but wasn't able to get any of them to work for my specific case. Any help is very welcome


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