Question

Jerry has an insurance policy with a premium of $150 per month. In June, he causes an accident and receives a bill with a total cost of $6000. His deductible is $1500, and his coverage limit is $10,000. Make an assumption about the relationship between coverage limit and premium. Explain your thinking.

Answer 1

Assumption: the monthly premium is (approximately) proportional to the coverage limit — i.e., higher limits cost proportionally more.

Why this is reasonable:
- The insurer’s expected dollar payout increases roughly in proportion to the coverage limit, so the premium (which funds expected payouts plus expenses and profit) will typically increase with the limit.
- Deductible, insured risk characteristics, and loading factors also matter, but for a simple model it is common to treat limit and premium as linearly related.

Numbers from this policy:
- Premium = $150/month buys a $10,000 coverage limit.
- That implies a unit rate of $150 / $10,000 = $0.015 per $1 of limit per month, or $15 per $1,000 of limit per month (=$180 per $1,000 per year).
- Under the June accident: $6,000 bill − $1,500 deductible = $4,500 paid by the insurer (since $4,500 < $10,000 limit); Jerry’s out‑of‑pocket for the claim is the $1,500 deductible (plus the premiums he pays).

If you need a different modeling assumption (e.g., nonlinear pricing, tiers, or a fixed base charge + per‑dollar charge), say so and I can use that instead.