  Many dark energy models fail to pass the cosmic age test because of the old
quasar APM 08279+5255 at redshift $z=3.91$, the $\Lambda$CDM model and
holographic dark energy models being no exception. In this paper, we focus on
the topic of age problem in the new agegraphic dark energy (NADE) model. We
determine the age of the universe in the NADE model by fitting the
observational data, including type Ia supernovae (SNIa), baryon acoustic
oscillations (BAO) and the cosmic microwave background (CMB). We find that the
NADE model also faces the challenge of the age problem caused by the old quasar
APM 08279+5255. In order to overcome such a difficulty, we consider the
possible interaction between dark energy and dark matter. We show that this
quasar can be successfully accommodated in the interacting new agegraphic dark
energy (INADE) model at the $2\sigma$ level under the current observational
constraints.
