#### Answer

$II$ is the preferred method of payment.

#### Work Step by Step

$I. A_I=1,000,000,000$ cents
$II.$ For 30 days, $A_{II}$=$1+2+4+...+2^{30-1}=\frac{2^{30}-1}{2-1}$ (GP with a=1, r=2, n=30)
$=1,073,741,824$ cents $\gt A_I$
$\therefore$ $II$ is the preferred method of payment.