A rate change for annual policies will affect policies sold during the period January 01, 2021 to December 30, 2023. You are given the following:

• There are no fixed underwriting expenses.
• Variable expenses are 25% of premium.
• Pure premium including LAE for policy year 2019 was $500.
• Loss inflation is 5% per year.

Using the pure premium method and a target profit percentage of 20%, determine the rate per exposure unit during the period January 01, 2021 to December 30, 2023.

• 826.86
• 890.46
• 909.09
• 1,027.24
• 1,052.36

According to the pure premium method, the indicated rate per exposure unit equals

[[math]] \overline{P_I} = \frac{\overline{L + E_L} + \overline{E_F}}{1 - V - Q_T} = \frac{\overline{L + E_L}}{0.55}. [[/math]]

The projection [math]\overline{L + E_L} [/math] equals $500 multiplied by the trend factor. To derive the trend factor, note that the midpoint of the experience period is the end of calendar year 2019 and the midpoint of the forecasting period is the end of calendar year 2022. Hence the trend factor equals 1.05 ³ = 1.1576 and the indicated rate per exposure unit equals

500 * 1.1576/0.55 = 1,052.36.