# House Insurance Payment

#### KWF

##### Junior Member
Explain how you determined the answer and the calculation used for determining the answer for the following:

A house is valued at $15,000. The owner insured it for$8,000 under a policy containing an 80% coinsurance clause. If a fire should cause a $7,500 loss to the house, how much would the owner receive under his policy? Answer$5,000

(The 80% coinsurance clause is applied to the value of the property, which $15,000. 80% of$15,000 is $12,000.) #### JeffM ##### Elite Member Explain how you determined the answer and the calculation used for determining the answer for the following: A house is valued at$15,000. The owner insured it for $8,000 under a policy containing an 80% coinsurance clause. If a fire should cause a$7,500 loss to the house, how much would the owner receive under his policy?

Answer $5,000 (The 80% coinsurance clause is applied to the value of the property, which$15,000. 80% of $15,000 is$12,000.)
Are you asking how co-insurance works or how to do the arithmetic?

#### KWF

##### Junior Member
Are you asking how co-insurance works or how to do the arithmetic?
How to do the arithmetic! How is the problem solved to determine the answer?

#### JeffM

##### Elite Member
So the insured was supposed to buy insurance totaling at least 80% of the value of the house.

The house was worth 15,000. 80% of 15,000 is 12,000.

Instead the insured bought insurance for only 8,000, which is 2/3rds of the minimum required.

The insured suffered an insured loss of 7,500. But the insurance company need pay only 2/3rds of the loss because the insured avoided paying a reasonable premium. So the insurance company is required to pay

(2/3) * 7500 = 5000.

The arithmetic is trivial.

#### KWF

##### Junior Member
So, the owner only insured it for 2/3 of its value and as a result when or if a loss occurs, the insurance company only pays that fractional amount (2/3 of the amount of loss) to the home owner, correct?

#### JeffM

##### Elite Member
No, the value of the house was 15K. The owner insured it for only 8k, which is considerably less than 2/3rds. But the owner is not required to insure for full value; only for 80% or more of full value. That is 12k in this case. The 8k which was insured is 2/3rds of the minimum required coverage so the insured only gets 2/3rds of the actual loss. The insured would have got the full loss had he paid premiums on 12k, which is not full value. Co-insurance penalizes only those policy holders who grossly underinsure.

#### KWF

##### Junior Member
Why is what I indicated in my last message/posting different from what you have replied to it? The two appear to express the same idea. (?)

#### JeffM

##### Elite Member
Why is what I indicated in my last message/posting different from what you have replied to it? The two appear to express the same idea. (?)
$$\displaystyle \dfrac{8000 \text{ insured value}}{15000 \text { actual value}} \text { is insuring for about 1/2 value, not 2/3 value.}$$

You are missing the basic logic behind co-insurance. The insurance company wants to receive a premium that is based on its potential payout, meaning the actual value of the property insured. The insured does not want to have to fight the insurer on what the exact value of the property is, nor does the insured want to pay a premium for a value in excess of the true market value. So the bargain is that there is no reduction in insurance proceeds if the property was insured at less than actual value, but not too much less (80% in this example). So the percentage reduction is based on the shortfall in insured value relative to the required minimum insured value, not the actual value. If your insured value equals or exceeds the required minimum, your losses are paid at 100% even if the insured value is less than the actual value. If you insure for less than the required amount, the amount paid is

$$\displaystyle \text {insurance payment} = \text {amount of loss } \times \dfrac{\text {insured value}}{\text {minimum required value}}.$$

The only relevance of actual value in the calculations is in determining the required minimum insured value.

KWF

#### KWF

##### Junior Member

Why is insurance payment = amount of loss x insured value/minimum required value the correct calculation but something like
insurance payment = minimum required value x insured value/amount of loss (or any other combination other than the correct calculation) would be incorrect?

I want to know more why the calculation insurance payment = amount of loss x insured value/minimum required value is the correct calculation not so much about co-insurance. Is this something that can be explained?

I thank you for your efforts and explanations that you have provided so far!

#### Subhotosh Khan

##### Super Moderator
Staff member
You do understand that by insuring for lower amount - the customer paid lower premiums. That was a risk that customer carried.

So during the loss payment period customer gets paid less.

#### Dr.Peterson

##### Elite Member
Why is insurance payment = amount of loss x insured value/minimum required value the correct calculation but something like
insurance payment = minimum required value x insured value/amount of loss (or any other combination other than the correct calculation) would be incorrect?
This is essentially a proportion. The rule says that the payment for a loss is proportional to the value:

insurance payment/amount of loss = insured value/minimum required value

So if you insure some fraction of the minimum (which is a stand-in for the actual value, as was explained), then you get that same fraction of the loss.

Solve this by your favorite method for solving proportions, and you get the stated formula. Any other formula would not satisfy the proportion (unless it was an equivalent calculation, such as doing the division before the multiplication).

KWF

#### JeffM

##### Elite Member
The formula translates into mathematical terms the contractual terms of the insurance policy. The whole point is to give arithmetic certainty to the specific purpose of the co-insurance clause. That purpose is to limit your coverage to what you actually paid premiums on.

Let's forget partial losses. And let's ignore deductibles, which were also ignored in your original example.

You have a house with a replacement cost of 800k. It is totally destroyed by fire. So your loss is 800k.

If you insured your house for 100k, you would have no reason to complain if the insurance company paid you only 100k, which is what you said the house was worth and what you paid premiums for. But if there is a coinsurance clause at 80%, you will actually get 125k, which is more than you said the house was worth.

What is the logic behind that. The insurance company says that they will pay the actual loss if you insure for at least 80% of true replacement cost. The company also says it will also cover part of the loss if you insure for less than 80%. What part? The closer you are to 80%, the bigger the part of the loss that is covered. To achieve that idea in an easy but unambiguous way, they take the ratio between the insured amount and the minimum required amount and apply that to the loss. in the case of a total loss, this means you get more than what you said the house is worth. (Again, this ignores deductibles.)

$$\displaystyle 800k \times \dfrac{100k}{640k} = 125k.$$

You can't really understand the formula if you don't understand what the purpose of coinsurance is.

#### KWF

##### Junior Member
This is essentially a proportion. The rule says that the payment for a loss is proportional to the value:

insurance payment/amount of loss = insured value/minimum required value

So if you insure some fraction of the minimum (which is a stand-in for the actual value, as was explained), then you get that same fraction of the loss.

Solve this by your favorite method for solving proportions, and you get the stated formula. Any other formula would not satisfy the proportion (unless it was an equivalent calculation, such as doing the division before the multiplication).
Yes, this is the type of reply/answer to my question that I wanted.

The result is as follows : amount of loss/minimum (required) value x insured value = insurance payment or amount of loss x insured value/minimum (required) value

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