A sinusoidal message signal having root mean square value of $4\:V$ and frequency of $\text{1 kHz}$ is fed to a phase modulator with phase deviation constant $2$ rad/ volt. If the carrier signal is $c\left ( t \right )=2\cos\left ( 2\pi 10^{6} t\right )$, the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is ________________ $\text{Hz}$.