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In Apple Numbers the app can work out the number of days between dates, but then if I times this by a number (ie, a %interest rate and an amount of money) Numbers insists that the answer is a number of days! Even if I go to Cell>Date Format and change it. The system ignores this and returns to displaying the answer as a number of days. How do I force the system to show this cell as a number and not in the date / days format?

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You can use a function to convert the duration to a plain number. For example, if difference between the dates in in E4, and it's 10 days, then...

=DUR2HOURS(E4) × 0.1

Shows a number, 24.0. There are other functions that you might use: DUR2DAYS, etc.

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=STRIPDURATION(your_current_forumula_resulting_in_days)*your_calculation_based_on_those_days

STRIPDURATION(duration-calculation) will give a number (of days), which you can then for a calculation.

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