That question frequently refers to a situation whereby interest is compounding at some frequency which is less than one year (monthly, quarterly, semiannually, e.g.) and one wishes to know what the equivalent effective annual rate is.
Letting r and m denote, respectively, the quoted annual rate and the number of compounding periods per year, then the effective annual rate is given by
(1 + r/m)^m - 1
For example, the effective annual rate for an annual nominal rate of 10% which compounds quarterly is
(1 + 0.10 / 4)^4 - 1 ≈ 10.38%.
In some scenarios the interest compounds continuously, which is to say that m → ∞ (the number of compounding periods per year approaches infinity). In such case, the effective annual rate is given by
e^r - 1
...where e is the natural log base, approximately 2.718281828. So a 10% nominal rate compounded continuously produces an effective annual rate of
e^0.10 - 1 ≈ 10.517%.
Caveat: Terminology is not at all standardized in the interest rate arena, and "annual compound interest rate" could also refer to something different than what I'm assuming here. It could, for example, refer to some interest rate which simply is compounded annually. Check the question's background very carefully to confirm exactly what's being asked.
