Nothing in finance is really continuous though. Most banks will calculate interest daily.

On a related note, I recently took the time to learn some financial Excel functions to create a Rent vs Buy spreadsheet.

It's worth anyone who ever keeps track of their finances using a spreadsheet to learn the FV function:

https://support.microsoft.com/en-us/office/fv-function-2eef9...

And the PMT function, which is useful for mortgage calculations:

https://support.microsoft.com/en-us/office/pmt-function-0214...