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

Region	Current relativity	Exposure Weight	Earned Premium at Current Rates	Projected Ultimate Loss
A	1.125	30%	421,875	375,000
B	1	50%	625,000	500,000
C	1.25	20%	312,500	300,000

Suppose the following is true:

• Policies are annual.
• Loss cost inflation is 4% per annum.
• There are no fixed or variable underwriting expenses.
• The insurer is targeting a profit percentage of 20%.

Using the loss ratio method, determine the rate change % for region A.

• +27.58%
• +28.15%
• +30.56%
• +31.17%
• + 32.97%

The midpoint of the experience period is 07/01/CY1 and the midpoint of the forecast period is the end of calendar year 3; hence, the trend factor equals 1.04^2.5 = 1.103 and the projected ultimate inflation adjusted losses for accident year 1 equals $1,296,025. Given a targeted profit percentage of 20% and an aggregate earned premium at current rates for accident year 1 equaling $1,359,375, the loss ratio method gives an overall change factor of 1.3111. The loss ratio method gives the following indicated rate differentials/relativities

Region [math]i[/math]	[math]\operatorname{R}_{I,i}/\operatorname{R}_{C,i} [/math]	[math]\operatorname{R}_{I,i}[/math]
A	1.1111	1.25
B	1	1
C	1.3021	1.6276

Given a targeted overall change factor of 1.3111, the change factor for the base rate equals

[[math]] 1.3111 \cdot \frac{\sum_i w_i \operatorname{R}_{C,i}}{\sum_i w_i \operatorname{R}_{I,i}} = 1.1877. [[/math]]

Hence the base rate should be increased by 18.77%. The rate change factor for region [math]i [/math] equals 1.1877 multiplied by [math]\operatorname{R}_{I,i}/\operatorname{R}_{C,i} [/math]:

Region [math]i[/math]	Rate Change
A	+ 31.97%
B	+18.77%
C	+54.65%