rate (n.)

early 15c., "estimated value or worth, proportional estimation according to some standard; monetary amount; a proportional part," from Old French rate "price, value" and directly from Medieval Latin rata (pars) "fixed (amount)," from Latin rata "fixed, settled," fem. past participle of reri "to reckon, think" (from PIE root *re- "to reason, count").

Meaning "degree of speed" (properly ratio between distance and time) is attested from 1650s. Currency exchange sense of "basis of equivalence upon which one currency is exchanged for another" is recorded by 1727. Meaning "fixed public tax assessed on property for some local purpose" is by 1712.

First-rate, second-rate, etc. are 1640s, from British Navy division of ships into six classes based on size and strength. Phrase at any rate originally (1610s) meant "at any cost," hence "positively, assuredly." weakened sense of "at least" is attested by 1760. Rate-payer "one who is assessed and pays a local tax" is by 1825.

rate (v.1)

"to scold, chide vehemently, rebuke," late 14c., raten, probably from Old French rateir, variant of reter "to impute blame, accuse, find fault with," from Latin reputare "to count over, reflect," in Vulgar Latin, "to impute, blame," from re- "repeatedly" (see re-) + putare "to judge, suppose, believe, suspect" (originally "to clean, trim, prune," from PIE root *pau- (2) "to cut, strike, stamp"). Related: Rated; rating.

Old French reter also was borrowed into Middle English as retten "to blame" (c. 1300); also "to attribute, impute" (late 14c.), "to consider, think about" (late 14c.).

rate (v.2)

"estimate the worth or value of, reckon by comparative estimation," mid-15c., raten, from rate (n.). Intransitive sense of "have a certain value, rank, or standing" is from 1809; specifically as "have high value" by 1928. Related: Rated; rating.

Definitions of rate
rate (n.)
a magnitude or frequency relative to a time unit;
they traveled at a rate of 55 miles per hour
the rate of change was faster than expected
rate (n.)
amount of a charge or payment relative to some basis;
a 10-minute phone call at that rate would cost $5
Synonyms: charge per unit
rate (n.)
the relative speed of progress or change;
he works at a great rate
Synonyms: pace
rate (n.)
a quantity or amount or measure considered as a proportion of another quantity or amount or measure;
the literacy rate
the dropout rate
the retention rate
rate (v.)
assign a rank or rating to;
The restaurant is rated highly in the food guide
Synonyms: rank / range / order / grade / place
rate (v.)
be worthy of or have a certain rating;
This bond rates highly
rate (v.)
estimate the value of;
Gold was rated highly among the Romans
How would you rate his chances to become President?
Synonyms: value