Elements of a Personal Automobile Insurance Policy - Part 6: Practice Questions and Solutions

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of Personal Insurance, cited below. Students are encouraged to read these pages before attempting the problems. This study guide is entirely an independent effort by Mr. Stolyarov and is not affiliated with any organization(s) to whose textbooks it refers, nor does it represent such organization(s).

Some of the questions here ask for short written answers based on the reading. This is meant to give the student practice in answering questions of the format that will appear on Exam 5. Students are encouraged to type their own answers first and then to compare these answers with the solutions given here. Please note that the solutions provided here are not necessarily the only possible ones.

Source:
Nyce, Charles, ed. Personal Insurance. (Second Edition). 2008. Chapter 4, pp. 4.6-4.25.

Original Problems and Solutions from The Actuary's Free Study Guide

Problem S5-104-1. Mr. Y has a personal automobile policy which provides coverage for transportation expenses in the event his insured vehicle is disabled due to a covered physical damage loss. There is a two-day waiting period specified, and the maximum the insurer will pay is $30 per day, up to a maximum of $1000 for transportation expenses resulting from each covered loss. Mr. Y's deductible for collision coverage is $500, and his deductible for "other than collision" (OTC) coverage is $200. Mr. Y's insured vehicle collides with a cow, which, in a fit of anger, decides to steal the vehicle and drive it away. The vehicle is missing for 6 days, whereafter it is found, and it is also discovered that the cow has significantly damaged the interior of the vehicle. It takes another 10 days to repair the damage. In the meantime, Mr. Y incurs expenses of $800 renting a car. How much will Mr. Y be reimbursed for transportation expenses by his insurer?

Solution S5-104-1. This question is based on the discussion in Personal Insurance, p. 4.6.

Transportation expenses are not subject to a deductible, so whether the loss is covered under collision or OTC coverage is not material to obtaining the desired result (the loss is probably covered under OTC coverage). Mr. Y incurred transportation expenses of $800 over 16 days, which amounts to 800/16 = $50 per day. But he can only be reimbursed up to $30 per day. Moreover, the two-day waiting period at the beginning of the 16 days reduces the number of days for which he will be reimbursed to 14. Thus, his total reimbursement for transportation expenses will be ($30/day)*(14 days) = $420.

Problem S5-104-2. Name five situations where the physical damage coverages of a typical personal automobile insurance policy would not apply.

Solution S5-104-2. This question is based on the discussion in Personal Insurance, p. 4.7-4.9. The following are all typical exclusions to the physical damage coverages of a typical personal automobile insurance policy:

1. "Public or livery conveyance" - i.e., the use of the insured's vehicle to carry people or property indiscriminately and for a fee;
2. "Damage 'due and confined' to wear and tear, freezing, mechanical or electrical breakdown or failure, and road damage to tires";
3. Damage due to war;
4. Damage due to radioactive contamination;
5. Damage to electronic equipment that is not permanently installed in the covered vehicle;
6. Damage to media and accessories that are not part of the vehicle;
7. Confiscation or destruction of the vehicle by governmental authorities;
8. "Physical damage loss to a trailer, camper, or motor home that is not shown on the declarations";
9. "Vehicles used without reasonable belief of being entitled" to do so;
10. Damage to radar and laser detection equipment;
11. "Loss to any custom furnishings or equipment in or on any pickup or van";
12. "Loss to a nonowned auto maintained or used " in a garage business;
13. Vehicles used in racing;
14. "Loss to, or loss of use of, a rental auto if the rental agreement includes a damage waiver or if applicable state law precludes the rental company from recovering from the insured for the loss."

Any five of the above suffice as an answer. Other valid answers may also be possible.

Problem S5-104-3. Mr. Q has a physical damage coverage on a trailer that he keeps in his living room as a decorative object. His collision deductible is $700, and his "other than collision" (OTC) deductible is $300. The trailer attracts the attention of a thief and is stolen during a break-in into Mr. Q's house. The trailer is never found and is declared a total loss. This loss is also found to be covered under Mr. Q's physical damage coverage and Mr. Q's homeowner's insurance, which has a sublimit of liability of $1,500 for trailers. It is estimated that the actual cash value (ACV) of the trailer was $2,200. Assume that Mr. Q wants to purchase a replacement trailer for $3,000. How much will be paid for this trailer by the following entities?

(a) Mr. Q's automobile insurer;
(b) Mr. Q's homeowners' insurer;
(c) Mr. Q.

Solution S5-104-3. This question is based on the discussion in Personal Insurance, p. 4.10.

(a) The automobile insurer's liability is limited to the actual cash value of the trailer, or $2,200. Because there are multiple sources of recovery, there is a pro rata sharing of losses between those sources based on the applicable limits. The homeowners' insurer has a limit of liability of $1,500 with respect to the trailer. The automobile insurer is thus only liable for 2200*(2200)/(2200 + 1500) = 1308.108108 = $1,308.11, of which Mr. Q must pay $300 of his OTC deductible (since theft is covered under OTC coverage, not collision coverage), meaning that Mr. Q's automobile insurer will pay $1008.11.

(b) On the basis of pro rata sharing of losses, Mr. Q's homeowners' insurer will pay 2200*(1500)/(2200 + 1500) = 891.8918919 = $891.89. There is no deductible applicable to this situation in the case of the coverage afforded by Mr. Q's homeowner's policy.

(c) Mr. Q has received from the two insurers 1008.108108 + 891.8918919 = $1,900. If he wishes to purchase the $3,000 trailer, he will have to pay the difference. Thus, Mr. Q will pay $1,100.

Problem S5-104-4.

(a) Name three general duties that an insured would have under a typical personal automobile policy in the event of a loss.

(b) Name two specific duties that an insured would have under the uninsured motorists coverage of a typical personal automobile policy in the event of a loss.

(c) Name two specific duties that an insured would have under the physical damage coverages of a typical personal automobile policy in the event of a loss.

Solution S5-104-4. This question is based on the discussion in Personal Insurance, pp. 4.19-4.21.

(a) The following are general duties that an insured would have under a typical personal automobile policy in the event of a loss:

1. Providing prompt notice to the insurer;
2. Cooperating with the insurer;
3. Submitting to the insurer notices or legal documents connected with the accident or loss;
4. Submitting to a physical examination at the insurer's expense, if requested to do so by the insurer;
5. Agreeing to examination under oath, if requested to do so by the insurer;
6. Authorizing release of medical records related to the claim, if requested to do so by the insurer;
7. Submitting proof of loss - "a statement of facts about a loss for which the insured is making a claim" (Personal Insurance, p. 4.20).

Any three of the above suffice as an answer. Other valid answers may also be possible.

(b) The following are specific duties that an insured would have under the uninsured motorists coverage of a typical personal automobile policy in the event of a loss:

1. Notifying the police promptly if a hit-and-run driver was involved in the accident;
2. Submitting to the insurer the legal documentation related to any suit against an uninsured motorist.

(c) The following are specific duties that an insured would have under the physical damage coverages of a typical personal automobile policy in the event of a loss:

1. Preventing further loss to the vehicle;
2. Notifying the police promptly in the event of theft;
3. Permitting inspection and appraisal.

Any two of the above suffice as an answer. Other valid answers may also be possible.

Problem S5-104-5.

(a) Name three kinds of changes during the policy term which may result in an adjustment to the premium for a personal automobile insurance policy?

(b) Mr. Φ has suffered a loss of $6,000 due to an at-fault motorist. Mr. Φ's insurer paid Mr. Φ the full $6,000 for the loss, and Mr. Φ was also able to obtain $2,000 from the at-fault motorist through a private agreement. How much will Mr. Φ be able to recover in total?

Solution S5-104-5. This question is based on the discussion in Personal Insurance, pp. 4.21-4.22.

(a) The following changes during the policy term may result in an adjustment to the premium for a personal automobile insurance policy:

1. Changes in the use, type, and number of insured vehicles;
2. Changes in the operators using the insured vehicles;
3. Changes in the place where the insured vehicles are principally garaged;
4. Changes in the coverages provided, the limits of liability, and the deductibles.

Any three of the above suffice as an answer. Other valid answers may also be possible.

(b) Mr. Φ will be able to recover $6,000, which is the amount of his loss. The insurer is entitled to subrogate against the at-fault motorist in order to recover all or part of its payment, and a typical personal automobile policy would require the insured to cooperate with the subrogation effort. The $2,000 from the at-fault motorist would be paid by Mr. Φ to the insurer, which may choose to attempt to recover the remaining $4,000 from the at-fault motorist.

See other sections of The Actuary's Free Study Guide for Exam 5.