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a prize, bonus, or award given as an inducement, as to purchase products, enter competitions initiated by business interests, etc.
a bonus, gift, or sum additional to price, wages, interest, or the like.
Insurance. the amount paid or to be paid by the policyholder for coverage under the contract, usually in periodic installments.
Economics. the excess value of one form of money over another of the same nominal value.
a sum above the nominal or par value of a thing.
the amount paid to the lender of stock by the borrower, typically a short seller.
the amount the buyer of a call or put option pays to the seller, quoted in dollars per share of stock.
a fee paid for instruction in a trade or profession.
a sum additional to the interest paid for the loan of money.
of exceptional quality or greater value than others of its kind; superior:
a wine made of premium grapes.
of higher price or cost.
of or relating to premiums:
to work in premium sales.
at a premium,

at an unusually high price.
in short supply; in demand:
Housing in that area is at a premium.

Contemporary Examples

Not, of course, if you have $487 to spend on the record-setting price tag attached to a premium orchestra seat.
‘The Book of Mormon’ Gives Back to the Faithful Jimmy So July 2, 2011

But the major bouts are all on premium cable or pay-per-view.
Why Spectators Sports Thrive or Die Michael Tomasky February 14, 2013

As a result, Livestream, without the consent of the team, upgraded the Global Revolution account to premium.
The Technology Propelling #OccupyWallStreet Sam Schlinkert October 5, 2011

She points to the far-reaching role media plays in our society and the premium placed on celebrity.
More Shocking Than Online Suicides Are the Crowds Who Clamor to Watch Caitlin Dickson December 9, 2013

Some services charge a fee for premium functionality, and sometimes, this functionality includes exporting the data.
Self-Tracking for N00bz Jamie Todd Rubin July 23, 2014

Historical Examples

Personal security was at too great a premium to leave much room for interest and speculation.
Gladiator Philip Wylie

Also, a premium can be contracted for, in the way of free association, for skilled labour.
Freeland Theodor Hertzka

Probably the extra five days was in the nature of a premium for the delay caused by the campaign, and the service in it.
Personal Recollections of the War of 1861 Charles Augustus Fuller

“I don’t believe they would give you the first premium,” said Cornelia.
The Coast of Bohemia William Dean Howells

Any subscriber sending us one NEW yearly subscriber will receive the bookshelf as a premium.
The Pansy Magazine, June 1886 Various

noun
an amount paid in addition to a standard rate, price, wage, etc; bonus
the amount paid or payable, usually in regular instalments, for an insurance policy
the amount above nominal or par value at which something sells

an offer of something free or at a specially reduced price as an inducement to buy a commodity or service
(as modifier): a premium offer

a prize given to the winner of a competition; award
(US) an amount sometimes charged for a loan of money in addition to the interest
great value or regard: to put a premium on someone’s services
a fee, now rarely required, for instruction or apprenticeship in a profession or trade
at a premium

in great demand or of high value, usually because of scarcity
above par

n.

c.1600, “reward given for a specific act,” from Latin praemium “reward, profit derived from booty,” from prae- “before” (see pre-) + emere “to buy,” originally “to take” (see exempt (adj.)). Insurance sense is 1660s, from Italian premio. Adjectival sense of “superior in quality” is first attested 1925, originally in reference to butter.
see:

at a premium
put a premium on