#### Answer

The answer is $\$1,073,741,823$.

#### Work Step by Step

Saving first day $=\$1$.
Second day $=\$2$.
Third day $=\$4$.
and so on.
The series is $1,2,4,8...$ this is the geometric series.
Common ratio is $r=2$.
The sum of the first $15$ days is
$S_{30}=\frac{1(1−2^{30})}{1−2}$
Simplify.
$S_{30}=1,073,741,823$.