Consumer Mathematics: Insurance

This chapter treats insurance as a mathematics problem: understanding risk, working out premiums, and calculating coverage and claims. It is a consumer-mathematics topic, so the goal is to compute the figures a question gives, not to give any real financial or insurance advice.

Questions describe a policy and ask you to compute a premium, a claim or a shortfall using the given rates. The maths is arithmetic; the difficulty is reading the terms carefully and applying exactly what the question states.

Insurance works by pooling: many policyholders each pay a small, certain premium so that the few who suffer a large, uncertain loss can be paid from the shared pot. That is why a premium is tiny next to the sum insured, you are buying protection against a chance, not the loss itself.

In a question the premium is usually a rate applied to the sum insured, for example a few ringgit per thousand of cover. Understanding the pooling idea helps the numbers make sense, but in the exam you still work strictly from the rates the question hands you.

Three terms control what a claim actually pays. The sum insured is the most the policy will pay.

An excess is a fixed amount you bear yourself before the insurer contributes, so it is subtracted from the payout. The average (co-insurance) clause bites when you under-insure: if the sum insured is less than the item's true value, the insurer pays only the same fraction of any loss, using payout = (sum insured ÷ value) × loss.

Miss any of these and your claim figure will be wrong even when the arithmetic is clean, so read the policy terms line by line.

Approach an insurance question like a checklist rather than a single formula. Write down the sum insured, the true value of the item, the size of the loss, any excess, and any co-insurance rate.

Apply the average clause first if the item is under-insured, then subtract any excess, and finally cap the result at the sum insured. Doing the steps in that order stops the common tangle of applying the excess and the average clause the wrong way round.

The maths is light; the marks live in reading the terms exactly and applying them in sequence.

This exam-style question tests the average (co-insurance) clause, a favourite twist in insurance problems.