These examples should help you use the two prefixes properly.
The magazine is published on a bi-monthly basis. (Every two months.)
Lawmakers are working on the state’s biennial budget.
(The budget period lasts two years. Note change in spelling.)
Semi-, on the other hand, refers to one-half of a time period.
We get paid on a semi-monthly basis. (That is, on the 15th and at the end of month. Do not confuse with bi-weekly, which is literally every two weeks.)
Enclosed is your semi-annual report for the period ending June 30, 2013.
(Note: Some sources also permit biannual in this usage.)
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