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%

Inflated adjusted projected ultimate losses for accident year 1 equals $1,500,000 multiplied by the loss trend factor. The midpoint of the experience period is 07/01/CY1 and the midpoint of the forecasting period is 08/01/CY3; hence, the trend factor equals 1.035 ^25/12 = 1.0743 and the Inflated adjusted projected ultimate losses for accident year 1 equals $1,611,450. According to the loss ratio method, the indicated rate change factor equals

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

By assumption, [math]Q_T = 0.15 [/math] and we have calculated above that [math]L/P_C [/math] equals $1,611,450 divided by $2,250,000 or 0.7162. Hence the the indicated change factor equals 0.8426 and the rate change is -15.74%.