'annual rate' is a compound of 'annual' and 'rate'. 'Annual' originates from Latin, specifically the word 'annualis' (from 'annus'), where 'annus' meant 'year'. 'Rate' originates from Old French/Medieval Latin (from Latin 'rata'/'ratus'), where the root related to a calculated or fixed value.

'annual' passed into English via Medieval Latin/Old French forms such as 'annualis' and Middle English 'annual'; 'rate' entered English from Old French (late) 'rate', from Medieval Latin forms based on Latin 'rata'/'ratus', eventually forming the compound phrase 'annual rate' in modern usage.

Initially, 'annual' simply meant 'of the year' and 'rate' meant 'a calculated value'; together the compound came to be used specifically for 'a value expressed per year' (the modern meaning).