A higher frequency of compounding leads to a higher effective rate of return. The effective rate of return with continuous compounding will, therefore, be greater than any effective rate of return with discrete compounding.

Detailed Explanation:

For a given stated annual rate of return (r):

1. Discrete compounding formula: Effective annual rate = (1 + r/m)^m - 1, where m is the number of compounding periods per year.

2. Continuous compounding formula: Effective annual rate = e^r - 1, where e is Euler's number (approximately 2.71828).

3. Mathematical relationship: As m increases (more frequent compounding), the effective rate increases. Continuous compounding represents the limit as m approaches infinity.

4. Example: For a stated annual rate of 10%:

   • Annual compounding (m=1): (1 + 0.10/1)^1 - 1 = 10.00%
   • Semiannual compounding (m=2): (1 + 0.10/2)^2 - 1 = 10.25%
   • Quarterly compounding (m=4): (1 + 0.10/4)^4 - 1 = 10.38%
   • Monthly compounding (m=12): (1 + 0.10/12)^12 - 1 = 10.47%
   • Continuous compounding: e^0.10 - 1 = 10.52%

Continuous compounding always yields the highest effective rate for a given stated annual rate.