= Solution
The <Stefan–Boltzmann law> gives the radiated <luminosity>
$$
L=4\pi R_\odot^2\sigma T_{\rm eff}^4\simeq3.69\times10^{26}\,\mathrm W.
$$
For <radiative mass loss at fixed luminosity>, using <mass-energy equivalence>, the mass-loss magnitude and one-percent time are
$$
\boxed{|\dot M|=L/c^2\simeq4.10\times10^9\,\mathrm{kg\,s^{-1}},\qquad t_{1\%}=\frac{0.01M_\odot c^2}{L}\simeq4.88\times10^{18}\,\mathrm s\simeq1.55\times10^{11}\,\mathrm{yr}.}
$$
The numerical constants are the external CODATA 2014 $\sigma=5.670367\times10^{-8}\,\mathrm{W\,m^{-2}K^{-4}}$ and $c=299792458\,\mathrm{m\,s^{-1}}$; years here mean 365.25 days.<CODATA recommended values of the fundamental physical constants 2014 by National Institute of Standards and Technology>[Stefan-Boltzmann constant and vacuum light speed]{ref} This estimates radiative mass loss with the supplied radius and <temperature> held constant. It does not predict a real stellar lifetime or include solar-wind mass loss.
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