Study for the SOA Fundamentals of Actuarial Mathematics (FAM) Exam. Prepare with flashcards and multiple choice questions with detailed explanations. Get ready for your future as an actuary!

Multiple Choice

In homeowners insurance with coinsurance, if the coinsurance requirement isn't met, the claim payment is given by which formula?

Coinsurance in property insurance requires you to carry a minimum amount of insurance relative to the property's value. When that minimum isn’t met, the claim payment is reduced proportionally to how much insurance you actually carried compared with what is required. The amount paid is the actual loss times the ratio of the insured amount to the required coverage, which is coinsurance times the value at the time of loss. In formula terms, payment = L × [amount covered / (coinsurance × value at time of loss)]. This captures the idea that underinsuring lowers the payout proportionally, while carrying the required amount would yield the full loss (subject to policy limits). For example, if the value is 100,000 and the coinsurance is 80%, the required coverage is 80,000. If you carried 60,000 and the loss is 20,000, you’d receive 20,000 × (60,000 / 80,000) = 15,000. The other forms don’t adjust by the correct ratio and would not reflect the coinsurance penalty correctly.

Coinsurance in property insurance requires you to carry a minimum amount of insurance relative to the property's value. When that minimum isn’t met, the claim payment is reduced proportionally to how much insurance you actually carried compared with what is required. The amount paid is the actual loss times the ratio of the insured amount to the required coverage, which is coinsurance times the value at the time of loss. In formula terms, payment = L × [amount covered / (coinsurance × value at time of loss)]. This captures the idea that underinsuring lowers the payout proportionally, while carrying the required amount would yield the full loss (subject to policy limits). For example, if the value is 100,000 and the coinsurance is 80%, the required coverage is 80,000. If you carried 60,000 and the loss is 20,000, you’d receive 20,000 × (60,000 / 80,000) = 15,000. The other forms don’t adjust by the correct ratio and would not reflect the coinsurance penalty correctly.