A leprechaun places a magic penny under a girl’s pillow. The next night there are 2 magic pennies under her pillow. Each night the number of magic pennies doubles. How much money will the girl have after 22 nights? How much money will the girl have after 22 nights? $\$ \square$

Step 1 ：Define the variables where \(a = 1\), \(r = 2\), and \(n = 22\).

Step 2 ：Calculate the sum of the geometric progression using the formula \(S = a \cdot \frac{r^n - 1}{r - 1}\), which gives \(S = 4194303.0\).

Step 3 ：Convert the total number of pennies to dollars by multiplying by 0.01, which gives \(money = 41943.03\).

Step 4 ：Final Answer: The girl will have \(\boxed{41943.03}\) dollars after 22 nights.