An insurer is considering a rate change that will be in effect for the next calendar year. The following is assumed:

• The projected ultimate loss and LAE ratio at current rates equals 75%.
• Fixed underwriting expenses are negligible.
• Variable expenses are 15% of premium.
• The target profit is 20% of premium.

If the insurer uses the loss ratio method for ratemaking, determine the % change in the rate.

• 14.75%
• 15.1%
• 15.38%
• 15.75%
• 16.33%

The indicated change factor equals

[[math]] ICF = \frac{(L + E_L)/P_C + E_F/P_C}{1 - V - Q_T} = \frac{0.75}{0.65} = 1.1538. [[/math]]

Hence the rate should be increased by 15.38%.