Render image on the fly vs. saving thumbnails

[eluser]obobo[/eluser]
I am working on a site that produces a lot of different sized thumbnails of user uploaded images. I haven't finalized the sizes yet, and new ones are bound to be introduced after the site launches.

Does it make sense in this scenario to render thumbnails on the fly every time they are displayed?
(ie: don't save them to the server, but create a thumbnail every time the image is displayed)

I've heard this approach defended by the idea that rendering every time on the fly is fine because it doesn't take up a lot of server time. But the script i've written to resize and send the thumb to the browser takes at best about .01 seconds to run. So on a page with 10 thumbnails i'm adding an extra second of server time to every page ... which seems significant enough to me when the original page only takes about .005 seconds to execute.

Rendering every time on the fly is convenient, but i'm not sure the convenience is worth the server time, or the fact that the images don't get cached on the user's computer.

I think i've answered my own question,
but any advice or insights appreciated.