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We are planning a two-month trip to Japan, at which time I'd like to purchase a computer for personal use. I would also like to permanently bring this computer back to the United States with me. Is there any issue with this?

I believe laptops are exempt from duty; is this correct? What about sales tax?

Thanks!

You may be able to buy the laptop duty-free and avoid sales-tax in Japan as you are a non-resident and leaving within six months. Unlike some countries, you are allowed to use tax-free purchased electronic devices in Japan while in-country. I bought a camera in Japan that I then used for a few weeks before returning to the USA. No one checks whether the seal on the camera box is still secure when you leave.

The federal government (customs) is mostly concerned whether the total value of items purchased abroad exceeds their personal-use exemption of US$800 per person (that is combinable, so if you were traveling with your spouse, you'd have a total of US$1600). Declare all of your purchases on your customs form and they'll do the calculations for you. It's best to declare everything and let them worry about the minutiae of classifications since obfuscating or leaving things out puts you at risk of being accused of smuggling.

Your state government may argue that you need to pay a 'use tax' equivalent to the state sales tax when you bring items back from out-of-state. However, enforcement of this tends to largely be voluntary so it will be up to you to declare this on your income tax form for your state (see Zach's note below in comments).

You would only pay sales tax at the time of sale (which is in Japan). So you would not pay sales tax again.

The CBP uses the Harmonized Tariff Schedule to determine duty rates:

The Customs Duty Rate is a percentage. This percentage is determined
by the total purchased value of the article(s) paid at a foreign
country and not based on factors such as quality, size, or weight. The
Harmonized Tariff System (HTS) provides duty rates for virtually every
existing item. CBP uses the Harmonized Tariff Schedule of the United
States Annotated (HTSUS), which is a reference manual that the
provides the applicable tariff rates and statistical categories for
all merchandise imported into the U.S.

You can search this database online and searching for computer or laptop does not return results that would indicate that there is duty to be paid for these items.

Anecdotal evidence (from many travels) indicates that computer laptops (especially if they are used like yours) are exempt.

Some of my US colleagues also purchase goods abroad and bring them to the US without issue - as they are cheaper here.

New ones, or multiple quantities of laptops do raise suspicions. My friend who was traveling with his family had 8 ipads, 3 laptops, 6 iphones and 2 android phones.

Other than a chuckle and questions as to what he was doing with so many things (till my friend pointed to this kids and wife), he did not have to pay any duties during his trip.