"estimated value or worth," early 15c., 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 first recorded 1727. 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;" weakened sense of "at least" is attested by 1760.
"to scold," late 14c., probably from Old French 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.
"estimate the worth or value of," mid-15c., from rate (n.). Intransitive sense of "have a certain value, rank, or standing" is from 1809; specifically as "have high value" from 1928. Related: Rated; rating.