  We examine a Friedmann-Robertson-Walker universe filled with interacting dark
matter, modified holographic Ricci dark energy (MHRDE), and a decoupled
baryonic component.The estimations of the cosmic parameters with Hubble data
lead to an age of the universe of $13.17 {\rm Gyr}$ and show that the MHRDE is
free from the cosmic-age problem at low redshift ($0 \leq z \leq 2$) in
contrast to holographic Ricci dark energy (HRDE) case. We constrain the
parameters with the Union2 data set and contrast with the Hubble data. We also
study the behavior of dark energy at early times by taking into account the
severe bounds found at recombination era and/or at big bang nucleosynthesis.
The inclusion of a non interacting baryonic matter forces that the amount of
dark energy at $z_{t} \sim {\cal O}(1)$ changes abruptly implying that
$\Omega_x (z\simeq 1100) =0.03$, so the bounds reported by the forecast of
Planck and CMBPol experiments are more favored for the MHRDE model than in the
case of HRDE cutoff. For the former model, we also obtain that at high redshift
the fraction of dark energy varies from 0.006 to 0.002, then the amount of
$\Omega_x $ at the big bang nucleosynthesis era does not disturb the observed
Helium abundance in the universe provided that the bound $\Omega_{x}(z\simeq
10^{10})<0.21$ is hold.
