Question

select the correct answer from each drop - down menu.
an automotive insurance company has 25,000 policyholders. the accident rate is 0.07.
the number of accidents the company will have to pay out for is
if the payout for each claim (after deductibles) is $8,000, the company’s total payouts will amount to $
if the company wants to keep a profit margin of 8%, the premium it must charge is $
the company can set aside a maximum amount of $ for this year’s investments.

Explanation:

Step1: Calculate number of accidents

Number of accidents = Total policyholders × Accident rate
$25000 \times 0.07 = 1750$

Step2: Calculate total payout amount

Total payout = Number of accidents × Payout per claim
$1750 \times 8000 = 14000000$

Step3: Calculate premium per policyholder

Let $x$ = premium per policyholder. Total premium = $25000x$.
Profit margin = 8% means total payout is 92% of total premium:
$14000000 = 0.92 \times 25000x$
First solve for $25000x$: $25000x = \frac{14000000}{0.92} \approx 15217391.30$
Then $x = \frac{15217391.30}{25000} \approx 608.69$

Step4: Calculate maximum investment amount

Maximum investment = Total premium - Total payout
$15217391.30 - 14000000 = 1217391.30$

Answer:

The number of accidents the company will have to pay out for is $\boldsymbol{1750}$.
The company's total payouts will amount to $\boldsymbol{\$14,000,000}$.
If the company wants to keep a profit margin of 8%, the premium it must charge is $\boldsymbol{\$608.69}$ per policyholder.
The company can set aside a maximum amount of $\boldsymbol{\$1,217,391.30}$ for this year's investments.