First, we need to calculate the monthly realized income:
\[ \text{Monthly Income} = \frac{\text{Annual Income}}{12} = \frac{36,864}{12} = 3,072 \]
Next, we calculate the fixed and housing expenses, which are 32% of the monthly income:
\[ \text{Fixed and Housing Expenses} = 0.32 \times \text{Monthly Income} = 0.32 \times 3,072 = 983.04 \]
Now, we calculate the savings, which are 15% of the monthly income:
\[ \text{Savings} = 0.15 \times \text{Monthly Income} = 0.15 \times 3,072 = 460.80 \]
To find the total discretionary money available excluding savings, we need to subtract both the fixed and housing expenses and the savings from the monthly income:
\[ \text{Discretionary Money} = \text{Monthly Income} - \text{Fixed and Housing Expenses} - \text{Savings} \]
\[ \text{Discretionary Money} = 3,072 - 983.04 - 460.80 = 1,628.16 \]
Thus, rounding to the nearest penny, the discretionary money available per month is:
\[ \boxed{1,628.16} \]