Etymology
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premium (n.)

c. 1600, "reward given for a specific act or a particular line of conduct," from Latin praemium "reward, profit derived from booty," from prae "before" (see pre-) + emere "to buy," originally "to take" (from PIE root *em- "to take, distribute").

The sense of "amount to be paid by agreement for a contract of insurance" is from 1660s, from Italian premio. The adjectival sense of "superior in quality" is first attested 1925, originally in reference to butter. Figurative use of the phrase at a premium "at more than the usual value" is by 1828.

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Definitions of premium
1
premium (n.)
payment for insurance;
Synonyms: insurance premium
premium (n.)
the amount that something in scarce supply is valued above its nominal value;
they paid a premium for access to water
premium (n.)
a fee charged for exchanging currencies;
Synonyms: agio / agiotage / exchange premium
premium (n.)
a prize, bonus, or award given as an inducement to purchase products, enter competitions initiated by business interests, etc.;
they encouraged customers with a premium for loyal patronage
premium (n.)
payment or reward (especially from a government) for acts such as catching criminals or killing predatory animals or enlisting in the military;
Synonyms: bounty
2
premium (adj.)
having or reflecting superior quality or value;
premium gasoline at a premium price
From wordnet.princeton.edu