is the annual continuous interest rate simply the semi annual continuous rate x 2?Thx

I would have thought it is (1 + semi-annual continuous rate) ^ 2 - 1.Although bear in mind that this is an opinion, rather than a definitive answer.

Uhm, yes: exp(r1)=exp(r2)exp(r2), where r1 is the 1 year rate and r2 is the half year rate. Take log's on both sides and r1=r2+r2=2*r2.GregWallace is referring to the semi-annually compounded rate. With semi-annual compounding against rate r2, the 1 year rate is r1 in: (1+r2)^2=1+r1, so (1+r2)^2-1 indeed.

A better term for "continuously compounded" interest rate is "log" interest rate. Then there is no confusion. Log interest rates are linear in time, which is one of the properties that makes them convenient.You have to be careful to distinguish how an interest rate is paid from how it is stated. Typically instruments are paid and stated over the same interval. An 8% coupon, $1,000 face bond will pay $80 per year, whether it pays annually, semi-annually, quarterly or monthly; because the coupon rate is stated over the same interval as the payment. Each of these will have a different log yield: 7.70%, 7.84%, 7.92% and 7.97% respectively.