A new survey by AlphaWise and Morgan Stanley polled 1,568 heads of U.S. households and found 11% are “extremely interested” and 36% are “somewhat interested” in an Apple-branded HDTV. Of those surveyed, 20% also said they would pay a premium to buy a TV from Apple (AAPL), suggesting there is an untapped market for Apple to offer up to 43 million HDTVs.

Before former CEO Steve Jobs passed away, he told his biographer Walter Isaacson that he was interested in a TV set with “the simplest interface” that syncs content from the iCloud. In a recent interview with NBC’s Brian Williams, CEO Tim Cook said TV was an area of “intense interest” for the company and coyly said “When I go into my living room and turn on the TV, I feel like I have gone backwards in time by 20 to 30 years.”

HDTVs aren’t cheap items, especially large-screened ones. According to the surveys, 46% of those polled said they would pay $1,000 for an Apple HDTV and 10% said they would pay over $2,000, with the average person surveyed willing to pay $1,060. The survey also revealed U.S. customers aged 18 to 29 are the most willing to buy a TV made by Apple and would pay a 32% premium.

Raymond Wong is a technology reporter with a passion for cutting-edge gadgets and clean design. He first realized his love for technology when he burned through so many AA batteries on the original Game Boy that scraping battery acid off it became the norm.