Pure Premium Method

$$\text{Indicated Avg Rate}=\frac{\text{Pure Premium including LAE}+\text{Fixed UW Expense Per Exposure}}{1-\text{Variable UW Expense \%}-\text{Target UW Profit \%}}$$

From the Fundamental Insurance Equation,

$$\begin{array}{rl}{P}_I& =L+E_L+(E_F+V\cdot P_I)+Q_T\cdot P_I\\ P_I-V\cdot P_I-Q_T\cdot P_I& =L+E_L+E_F\\ P_I(1-V-Q_T)& =L+E_L+E_F\\ P_I& =\frac{L+E_L+E_F}{1-V-Q_T}\end{array}$$

Divide by the number of exposures to find the indicated average premium per exposure, $X$:

$$\overline{P_I}=\frac{\overline{L}+{\overline{E}}_L+{\overline{E}}_F}{1-V-Q_T}$$