Answer
Please see the work below.
Work Step by Step
According to law of conservation of energy
$L_i\omega_i=L_f \omega_f$
$\implies (\frac{2}{5}mr_i)^2(\frac{2\pi}{T})=(\frac{2}{5}mr_f^2)(\frac{2\pi}{T_f})$
This simplifies to:
$\frac{r_i^2}{T_f}=\frac{r_f^2}{T_f}$
$\implies T_f=\frac{r_f^2}{r_i^2}T_i=\frac{(7\times 10^8)^2}{(1\times 10^{13})^2}(1.4\times 10^6)=0.00686yr$
