In addition to effective annual rates, there are also effective periodic rates (EPR).
What would be the appropriate effective periodic rate (EPR)?
What is the appropriate effective periodic rate (EPR) for the client to be able to solve for an estimated future value?
As part of our investigation on auditory processing in the toadfish (e.g., 2), we have evaluated the sensitivity of the auditory midbrain (torus semicircularis, TS) to sound pulses produced at several periodic rates
. The stimuli for our previous experiments have been various frequencies of sinusoidal particle motion (described in 3).
A simpler formula applies with constant periodic rates,
where, the geometric averages G and K are equal to the respective periodic rates. It is trivial that a unique NDR exists that satisfies equation (2),
More importantly, with time-varying periodic rates an exact historical NDR may be obtained from equation (4).
Simplifying, and expressing the relationship in risk premia for, we obtain:  [Mathematical Expression Omitted] where [Mathematical Expression Omitted] Hence, consistent and unbiased estimates of CAPM parameters can be obtained by relating the rate of change in the geometric mean of asset value to the geometric mean of the true periodic rates of return for the market portfolio and risk-free asset.(5)
Essentially the same series of average market and risk-free rates of return are obtained whether they are calculated as geometric or arithmetic averages of true periodic rates, or as the rate of change in arithmetic period-average value.