Insurance Exam Math: The Formulas You Need, With Worked Examples

Insurance exam math is not hard, but it is unforgiving: one step in the wrong order gives you a wrong answer that looks plausible. The same few formulas cover most of it. Here they are, with the sources behind the definitions and problems you can check yourself.

Quick answer: Know five calculations: actual cash value, the replacement cost holdback, a percentage deductible, the coinsurance penalty, and the hurricane deductible carryover. Do them in a fixed order and write each step down.

The five formulas

Calculation	Formula	Source for the rule
Actual cash value (ACV)	Replacement cost − depreciation	TDI glossary
Replacement cost payment	First payment = replacement cost − depreciation − deductible; the depreciation is released after repairs are completed	Maryland advisory
Percentage deductible	Dwelling limit × percentage (not the claim amount)	Texas OPIC
Coinsurance	(Carried ÷ required) × loss − deductible, where required = value × percentage	Maine consumer guide, as we read it
Hurricane deductible, second storm	Greater of the unmet balance or the all other peril deductible	Florida CFO

Problem 1: actual cash value

A policy pays on an ACV basis. The loss costs $18,000 to repair. Depreciation is 35 percent. The deductible is $500. What does the insurer pay?

Depreciation = $18,000 × 0.35 = $6,300. ACV = $18,000 − $6,300 = $11,700. Payment = $11,700 − $500 = $11,200.

Problem 2: replacement cost with a holdback

Same loss, but the policy pays replacement cost and the insured completes the repairs. What is the first payment, and what is the total?

First payment = $18,000 − $6,300 − $500 = $11,200. After the work is done the held-back $6,300 is released, for a total of $17,500 ($18,000 − $500).

Problem 3: percentage deductible

A dwelling is insured for $240,000 with a 2 percent wind and hail deductible. Wind causes $9,000 in damage. What does the insurer pay? What if the damage is $4,000?

Deductible = $240,000 × 0.02 = $4,800. For $9,000: $9,000 − $4,800 = $4,200. For $4,000: the damage is below the deductible, so the insurer pays $0.

Problem 4: coinsurance with a penalty

A building has a replacement cost of $500,000. The policy has an 80 percent coinsurance clause and $300,000 of coverage. A fire causes a $60,000 loss. The deductible is $1,000.

Required = $500,000 × 0.80 = $400,000. Ratio = $300,000 ÷ $400,000 = 0.75. Payment = 0.75 × $60,000 = $45,000, minus $1,000 = $44,000.

Problem 5: coinsurance with no penalty

Same building and loss, but the owner carries $400,000. Ratio = $400,000 ÷ $400,000 = 1.00. Payment = $60,000 − $1,000 = $59,000.

Problem 6: Florida hurricane deductible

A Florida home is insured for $300,000 with a 5 percent hurricane deductible. A hurricane causes $40,000 of damage. The deductible is $15,000, so the insurer pays $25,000. If a second hurricane hits later the same year, the first deductible was fully met, and the policy's all other peril deductible is $1,000, a $20,000 loss pays $19,000.

All the dollar figures in these problems are our own illustrations. Only the rules come from the sources above.

Exam habits that save points

1. Write the order of operations first. Ratio or percentage, then loss, then deductible.
2. Check what the percentage applies to. Percentage deductibles use the dwelling limit, and coinsurance uses the property's value.
3. Read for the policy basis. ACV or replacement cost changes the answer.
4. Sanity-check. A payment bigger than the loss is wrong, and so is one bigger than the limit.
5. Know your state's outline. Formulas are standard, but each state's exam covers its own law too.

Try it on real exam questions

Every state's exam is different, and the best way to learn these calculations is to practice them. Take 20 free practice questions for your state, scored instantly with explanations: Alabama, Alaska, Arizona, Delaware, District of Columbia, Hawaii, Idaho, Iowa, Kansas, Louisiana, Maine, Maryland, Massachusetts, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Mexico, North Carolina, North Dakota, Oklahoma, Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Utah, Vermont, Virginia, Washington, Wyoming.

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Related reading

• The Coinsurance Clause Explained: The Penalty Formula, With Examples
• Actual Cash Value vs. Replacement Cost: What Each One Pays
• How Insurance Deductibles Work: Flat, Percentage and Hurricane Deductibles
• Why Do People Fail the Insurance License Exam?
• How to Become a Claims Adjuster With No Experience