Formulas for Focal Lengths

Last year I bought a Canon Powershot A590 IS. I came across an article regarding determination of effective aperture i.e. f= F/D (F= focal length & D= diameter of effective aperture). Going by this, I got the right effective aperture of  f/2.6 at wide-end (the focal length of the lens is 5.8-23.2mm).But the effective aperture value at tele end baffled me. The calculations came to f/10.5. The aperture my camera actually allows is f/8. Is this a limitation of a compact cameras or its an error on my part?
Sadashib Mukherjee, via email

The equations work with simple lenses, single lens elements and prime lenses. A compound lens with moving elements, like the zoom lens of your camera, is more complicated to define with a standard equation. Lenses are designed to help you shoot. Lens characteristics are hugely dependant on their design. The lens of your camera has been constructed to give you a stop of advantage at the telephoto-end.