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 { ~ { } 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 .