Obviously, you ask them. List out all of the reason it would be so helpful especially since its summer. But even if they say no, first you want to get the idea in there head and keep on telling them you want it each day. Also, list out what you would be willing to give up or give in.
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Maybe by explaining to them what you are going to do to help pay for it and maintain it.
Well, swimming is a sport so it will help you get/stay healthy and fit, swimming is really fun, and even they could enjoy swimming!
Hope this helps:)