Calulating refunds

Tenancy Types and Management

I want to know what is the industry standard for calculating overpayments if the tenant leaves earlier than their rent period ends.

in this case the new tenant wanted to move in quickly so the previous tenant who knew her agreed to move out 4 days early.

Is it calculated on monthly rent x 12 months divided by 365 to get the daily rate then x days they didn't live there (in this case 4)OR number of days she has stayed there in that rent period. If its worked out the second way it comes out at a different figure if its a long month like August.

Also, if there is a handover on the same day how is the rent worked out.

We have always worked it out on a daily rate and refunded the number of days the tenant didn't live there but new software is working out on the number of days they have lived there in that rent period.

Advice needed please.