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%

An insurer is considering a rate change for annual policies effective Nov 01 of Calendar year 2 to June 30 of Calendar year 3. The insurer uses the loss ratio method for ratemaking. The insurer assumes the following:

• Projected accident year 1 ultimate losses equal $1,500,000.
• Accident year 1 earned premium at current rates equals $2,250,000.
• The effective annual loss cost inflation rate equals 3.5%.
• There are no fixed and variable expenses.
• The target profit percentage is 15%.

Determine the rate change.

• -16.24%
• -15.98%
• -15.84%
• -15.74%
• -15.24%

An insurer is considering a rate change that will be in effect during calendar year 3. The insurer uses the loss ratio method for ratemaking. The following is true:

• Projected accident year 2 ultimate losses equal $1,500,000.
• Accident year 2 earned premium equals $1,700,000.
• The last rate change was at the beginning of calendar year 1.
• Loss cost inflation equals 4% per annum.
• There are no fixed underwriting expenses.
• Variable expenses equal 10% of premium.
• The target profit percentage is 15%.

Determine the rate change.

• +22.36%
• +22.64%
• +23.56%
• +24.25%
• +24.78%

An insurer is considering a rate change that will be in effect during calendar year 4. The insurer uses the loss ratio method for ratemaking and has access to the following historical loss data for accident year 1:

Historical rate changes are given below:

The following is assumed:

• Earned premium for accident year 1 equals $3,000,000.
• Policies are annual and written evenly throughout the year.
• Loss cost inflation equals 3% per annum.
• Accident year losses are fully developed three years after the end of the accident year.
• There are no fixed or variable underwriting expenses.
• The target profit percentage is 15%.

Determine the rate change.

• -34.33%
• -33.75%
• -32.33%
• -31.5%
• -29.75%

An insurer is considering a rate change that will be in effect during calendar year 4. The insurer uses the loss ratio method for ratemaking and has access to the following historical loss data for accident year 2:

Historical rate changes are given below:

The following is assumed:

• Ultimate losses for accident year 2 losses are projected to be 25% higher than accident year 2 reported losses.
• Earned premium for accident year 2 equals $1,500,000.
• Policies are annual and written evenly throughout the year.
• Loss cost inflation equals 3% per annum.
• There are no fixed or variable underwriting expenses.
• The target profit percentage is 15%.

Determine the rate change.

• +25.17%
• +26.31%
• +27.11%
• +28.25%
• +29.15%

An insurer is considering a rate change that will be in effect during calendar year 3. The insurer uses the loss ratio method for ratemaking. The following is true:

• Projected policy year 1 ultimate losses equal $1,250,000.
• Policy year 1 earned premium equals $1,400,000.
• Rates were increased by 5% on July 01 of calendar year 1 and then increased again by 3% on July 01 of calendar year 2.
• Policies are annual and written evenly throughout the year.
• Loss cost inflation equals 3% per annum.
• There are no fixed underwriting expenses.
• Variable expenses equal 10% of premium.
• The target profit percentage is 20%.

Determine the rate change.

• +28.17%
• +28.95%
• +29.33%
• +29.91%
• +30.55%

An insurer uses classification ratemaking to set rates and uses a single rating variable to classify policies with three different levels: level I, level II and level III. The pure premium for each level is assumed to be gamma distributed with unknown parameters [math]\theta [/math] and [math]\alpha [/math] that change across levels. More precisely, we have the following:

Marketing wants level II rates to be 10% higher than level 1 rates and level III rates 15% higher than level I rates. If the insurer targets an expected profit percentage of 15% and there are no fixed or variable expenses, determine the rate per exposure unit for level II policies.

• 1,379.92
• 1,450.56
• 1,457.25
• 1,516.49
• 1,578.22

An insurer uses classification ratemaking to set rates and uses a single rating variable to classify policies with three different levels: level I, level II and level III. The base level is level I. The pure premium for each level is assumed to be gamma distributed with unknown parameters [math]\theta [/math] and [math]\alpha [/math] that change across levels:

If the insurer wants an overall rate increase of 10% and there are no fixed or variable expenses, determine, using the pure premium method, the rate change % for level III policies.

• +2.16%
• +2.78%
• +3.25%
• +3.78%
• +4.11%

The exposure is split into three geographic regions: region A, region B and region C. The following accident year 2 data is available:

The insurer is targeting an 8% overall increase in rates. Using the pure premium method, determine the rate change % for region A.

• +4.87%
• +5.05%
• +5.53%
• +5.9%
• +6.33%

The exposure is split into three geographic regions: region A, region B and region C. The following accident year 1 data is available:

Suppose the following is true:

• Policies are annual.
• Loss cost inflation is 4% per annum.
• The insurer is targeting an 12% overall increase in rates.

Using the loss ratio method, determine the new rates, effective for calendar year 3, for region C.

• 124.55
• 128.66
• 130
• 137.25
• 155.4