Basket recalculation on the fly depending on delivery option

I’ve added another delivery option and wondering how can I update the total cost of the basket on the fly if I change delivery option, are there any examples? I have not found.
Should I send POST request on option change.or add some custom code?
Here is my situation:

Thanks in advance.

If there is no solution I’m going to fix it on my own…as soon as I finished I’ll share the result and how it works.

Just to confirm, SimpleCart does not have this type of behavior available.

It does calculate the total price when rendering the various shipping options. If you format those in a specific way (perhaps adding them as data attributes on the radio input), you could fetch those and dynamically update your cart summary with javascript.