An insurer is conducting a rate review study to set rates for the period Jan 01, 2021 to June 30,2022. The insurer uses the loss ratio method for ratemaking and relies on historical data to project losses. The insurer is given the following:

• Policies are annual.
• Policy year 2018 ultimate losses equaled $650,000.
• Policy year 2018 earned premium at current rates equals $900,000.
• Annual loss inflation equals 2%.
• Variable expenses equal 10% of premium.
• Fixed underwriting expenses are negligible.

If the insurer is targeting a profit equaling 20% of premium, determine the % change in the rates.

• -5.195%.
• 0%
• 7.75%
• 8.96%
• 9.5%

The experience period is policy year 2018 and the midpoint of the experience period is 01/01/2019. The forecasting period is 01/01/2021 to 06/30/2022 with a midpoint equal to 10/01/2021. Hence the trend factor equals 1.02 ^2.75 = 1.056 and the projected loss ratio, [math] L /P_C [/math], equals

1.056*650,000/900,000 = 0.7627.

According to the loss ratio method, the indicated change factor equals

[[math]] ICF = \frac{(L + E_L)/P_C + E_F/P_C}{1 - V - Q_T} = 0.7627/0.7 = 1.0896. [[/math]]

Hence rates should be increased by 8.96%.