  We present precise path-integral Monte-Carlo results for the thermodynamics
of a homogeneous dilute Bose gas. Pressure and energy are calculated as a
function of temperature both below and above the Bose-Einstein transition.
Specifically, we address interaction effects, focusing on deviations from the
ideal gas law in the thermodynamic limit. We also calculate the isothermal
compressibility and the contact parameter, which provide a clear signature of
the role played by interactions. In particular, we show that the
compressibility exhibits a discontinuity at the transition point. To gain
physical insight, numerical results are systematically compared with the
predictions of first-order Hartree-Fock and second-order Popov theories, both
giving an approximate description of the gas thermodynamics. The comparison
shows the extension of the critical region around the transition point, where
the inaccuracies of the perturbative expansions are more pronounced.
