Under-insurance means you insured for less than the policy requires, so the insurer pays a proportion of the loss. The formula does the work; three sense checks tell you whether the result can be right.
This lesson is part of insurance mathematics. The claim steps it builds on are in calculating a claim using stated policy conditions.
What is the formula, as used in this lesson?
Use the formula as your question supplies it. In this lesson’s worked example it is:
Payment = (amount insured ÷ required amount) × loss, where required amount = co-insurance % × property value.
If the amount insured is at least the required amount, the loss is paid in full and the formula is not used.
Worked example: a house claim
An original policy: property value RM300 000, co-insurance 80%, amount insured RM180 000. The loss is RM40 000.
Step one, required amount: 80% × 300 000 = RM240 000. Step two, compare: 180 000 is below 240 000, so there is under-insurance.
Step three, payment: (180 000 ÷ 240 000) × 40 000 = 0.75 × 40 000 = RM30 000. The policyholder bears the remaining RM10 000.
What are the three sense checks?
- The payment must not be more than the loss: 30 000 is below 40 000.
- The payment must not be more than the amount insured: 30 000 is below 180 000.
- The proportion must be below 1 when under-insured: 0.75 is below 1.
If any check fails, a step was misapplied. The checks take under fifteen seconds.
The mistake that passes unnoticed
A student divides by the property value instead of the required amount: 180 000 ÷ 300 000 = 0.6, then 0.6 × 40 000 = RM24 000. The working looks tidy and passes all three sense checks.
The error sits in the denominator. Write “required = 80% × 300 000” as its own line so the denominator is never the property value by habit.
A second error applies the formula when the insured amount is enough. With RM260 000 insured, (260 000 ÷ 240 000) × 40 000 = RM43 333, which is more than the loss. Check one catches it, and the correct payment is the full RM40 000.
A self-check question
Property value RM500 000, co-insurance 90%, amount insured RM360 000, loss RM25 000. Find the payment.
Answer
Required amount: 90% × 500 000 = RM450 000. The insured amount is below that, so payment = (360 000 ÷ 450 000) × 25 000 = 0.8 × 25 000 = RM20 000. Checks: 20 000 is below the loss and below the amount insured, and 0.8 is below 1.
Try the mixed questions in the insurance practice set. If the percentage step slows you, the algebra step repair trainer drills it.
For help using formulas on your own textbook questions, SPM Mathematics one-to-one tuition lets a teacher check your substitutions line by line.