A premium is what you pay to hold a policy. A deductible is what you pay first on a claim, and co-insurance is a shared percentage of what remains. Keep them apart and most insurance questions open up.
This lesson is part of insurance mathematics in SPM Mathematics.
Who pays what?
| Term | Who pays | When |
|---|---|---|
| Premium | Policyholder | Regularly, to keep the policy |
| Deductible | Policyholder | First part of each claim |
| Co-insurance (shared percentage) | Policyholder and insurer | On the amount left after the deductible |
A yearly premium of RM1 200 is RM100 a month, since 1 200 ÷ 12 = 100.
Worked example: one medical bill
An original policy: the deductible is RM1 000 and the policyholder pays 20% of the remaining bill (co-insurance). The hospital bill is RM10 000.
Step one, subtract the deductible: 10 000 − 1 000 = RM9 000. Step two, find the shared part: 20% × 9 000 = RM1 800.
The policyholder pays 1 000 + 1 800 = RM2 800. The insurer pays 10 000 − 2 800 = RM7 200.
Check: 7 200 + 2 800 = 10 000, the whole bill.
The mistake that costs marks
The common slip is taking 20% of the whole bill: 20% × 10 000 = RM2 000, then adding the deductible to get RM3 000. The policyholder then seems to pay RM200 too much.
The cause is reading “co-insurance” without the phrase “of the remaining bill”. Circle the phrase that tells you what the percentage applies to before you calculate.
Two meanings to watch for
Some questions use co-insurance for a condition on property cover, where the insured amount must reach a stated percentage of the property’s value. That meaning leads to the ratio method in checking under-insurance calculations.
The two meanings work differently, so check which one the question uses. The wording always says.
A self-check question
A bill is RM8 000. The deductible is RM500 and the policyholder pays 10% of the remaining bill. The yearly premium is RM1 140. Find how much the insurer pays, and the monthly premium.
Answer
Remaining bill: 8 000 − 500 = RM7 500. The policyholder’s 10% share is RM750, so the policyholder pays 500 + 750 = RM1 250. The insurer pays 8 000 − 1 250 = RM6 750. Monthly premium: 1 140 ÷ 12 = RM95.
Next, practise the order of conditions in calculating a claim using stated policy conditions. The graph evidence comparison lab helps if the question shows the data as a table or graph.
If policy wording keeps tripping you, SPM Mathematics one-to-one tuition can start from your own textbook pages.