Apple shares closed above US$700 for the first time on Tuesday on the back of the popularity of the new iPhone 5. Apple shares closed at $701.91 on the Nasdaq, up $2.13 or 0.3 percent from the previous session.

That brings Apple's total market capitalization to $658 billion, making it the most valuable company on both the New York Stock Exchange and Nasdaq.

Apple shares rose above $600 in early August. News that sales of the new iPhone surpassed 2 million units on the day of its release gave it the additional push.

Apple has released one new smartphone and one new tablet PC a year, and shares perform according to the timing of the release and the response of consumers. Shares surged in March just before the April launch of the New iPad and began another ascent in August, when there were rumors of an impending launch of the iPhone 5. Barclays Bank recently raised its share price forecast for Apple from $750 to $810.

Expectations for the iPhone 5 are growing. Morgan Stanley forecast sales of the gadget to reach between 48 and 50 million within three months of its release, while CNN Money projected sales of 45 million units.