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%

Since the last rate change was at the start of calendar year 1 and the policies are annual, the accident year 2 earned premium at current rates is the same as accident year 2 earned premium or $1,700,000. The midpoint of the experience period is 07/01/CY2 and the midpoint of the forecasting period is the end of calendar year 3; hence the trend factor equals 1.04 ^1.5 = 1.0606 and the inflation adjusted projected ultimate losses for accident year 2 equal $1,590,894. 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}{0.75} [[/math]]

with [math]L/P_C [/math] equal to $1,590,894 divided by $1,700,000. Hence the indicated change factor equals 1.2478 and the rate should be increased by 24.78%.