Hmm, I get close to that interest if we assume that interest is compounded semiannually but paid only annually.

If we assume that the interest is compounded semiannually, that means the interest is applied twice a year to the total balance payable (principal plus any accrued interest).  In that situation, with an effective rate of 7.74%, after 1 year, the balance is 1.0774 times what it originally was.  This was after two compoundings.  Let r be the semiannual stated rate.
Then (1+r)*(1+r) = 1.0774
(1+r)^2 = 1.0774
1+r = sqrt(1.0774) = 1.0379788
r = 0.0379788
This is the semiannual stated rate.  To get the annual stated rate, multiply by 2:
2*0.0379788 = 0.07595761
rounds up to 7.6%

However, if the interest is payable and paid semiannually, then interest accrues only on the principal amount, and the stated rate would be the same as the effective rate??  What is Becker's explanation?