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%

Since policies are assumed to be written evenly throughout the year, the earned premium at current rates for policy year 1 equals the earned premium, $1,400,000, multiplied by

(6/12)*1.03*1.05 + (6/12)*1.03 = 1.05575

or $1,478,050. The midpoint of the experience period is the end of calendar year 1 and the midpoint of the forecast period is the end of calendar year 3; hence the loss trend factor equals 1.03² = 1.0609 and the projection for the ultimate inflation adjusted policy year 1 losses equals $1,326,125. 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} = \frac{L/P_C}{0.7} [[/math]]

with [math]L/P_C [/math] equal to $1,326,125 divided by $1,478,050. Hence the indicated change factor equals 1.2817 and the rate change is +28.17%.