[Underwriting and Rating: Setting Insurance Rates]If thenet premiumis $4,000 and thebroker’s commissionis 20%, what is...

Anet premiumis the amount remainingafter commission is deducted. Therefore, the policy premium must behigherthan the net premium, because the insurer must pay the broker their commission out of the gross premium.

Formula:

Net Premium=Policy Premium×(1−Commission Rate)\text{Net Premium} = \text{Policy Premium} \times (1 - \text{Commission Rate})Net Premium=Policy Premium×(1−Commission Rate)4,000=P×0.804,000 = P \times 0.804,000=P×0.80P=4,0000.80=5,000P = \frac{4,000}{0.80} = 5,000P=0.804,000​=5,000

Thus, the policyholder must be charged$5,000, so that:

$1,000 (20%) goes to the broker, and

$4,000 remains as the net premium for the insurer.

Correct answer:C: $5,000.