Gce Model Questions Vol1 2021 Commerce Question 10

Practice essay / theory question 10 from the 2021 Gce Model Questions Vol1 Commerce examination. This question covers Insurance, Risk Management, Probability, Financial Mathematics .

Gce Model Questions Vol1 2021 Commerce Essay / Theory
Topics: Insurance Risk Management Probability Financial Mathematics
Question 10 GCE_MODEL_QUESTIONS_VOL1 • 2021 • COMMERCE • essay

A motor insurance company offers a comprehensive policy with the following features: - Annual premium: ₦120 000. - Deductible (excess) per claim: ₦15 000. - No‑Claim Bonus (NCB) discount: 5 % reduction in premium for each claim‑free year, up to a maximum of 25 %. - Probability of a claim in any given year for a typical policyholder: 0.08. - Average cost of a claim (before deductible) for the company: ₦250 000. Assume the policyholder, Mr. Bello, has been claim‑free for the past two years. Answer the following:

Question Parts

( a )
Calculate the expected annual cost to Mr. Bello (including premium, NCB discount, and expected out‑of‑pocket expense) for the upcoming policy year.
( b )
If the company raises the deductible to ₦30 000 while keeping the premium unchanged, determine the new expected annual cost to Mr. Bello and comment on how the change affects his expected out‑of‑pocket expense and the insurer’s risk exposure.
( c )
Assuming Mr. Bello remains claim‑free for the next three consecutive years, calculate the premium he would pay in the fourth year, showing the effect of the maximum NCB discount.
( d )
Critically evaluate the fairness of using a deductible and NCB system from both the insurer’s and the policyholder’s perspectives.

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About This Question

This is Gce Model Questions Vol1 2021 Commerce Question 10. It is one of the essay questions from the 2021 Gce Model Questions Vol1 Commerce examination.

The question covers Insurance, Risk Management, Probability, Financial Mathematics .

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