Ah, this was very helpful, thanks. Not being too clever in these matters, I didn't quite understand the above, but it got me close enough to experiment successfully (though I don't quite get the second bullet item). In my case I was after an offset to add to a unixtime, so that's how the code is oriented.

for (my $i = 0; $i < 60; $i++) {

    my $offset = getOffsetToNearestInterval($i,15);
    print "$i: " . ($i + $offset) . ' (' . $offset . ')' . "\n";

}

sub getOffsetToNearestInterval {

    my $number = shift;
    my $interval = shift;

    my $nearest_interval = ( $interval * int( ($number + ($interval/2)
+ ) / $interval) );
    my $offset_to_interval = $nearest_interval - $number;

    return $offset_to_interval;
}
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Hope this helps the next guy stumbling on this thread.