Help with calculating Pro-Rata Premium

tsims25

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Dec 31, 2015
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Hi, I'm trying to do an exercise by calculating the pro-rata premium with endorsements but I'm a little confused.

I have an annual premium of $1,500 which a customer paid in full on November 1, 2017.
Part of the premium included an endorsement that was fully earned and paid, that premium was $200 of the $1500.
The insured party sold their house on June 1, 2018 and cancelled their policy on that date.

I have to calculate the returned premium. Here's how I did it but not sure if it's correct:

$1,500/365 = $4.11/day
$4.11 x 212 days . = $871.32

So they returned premium will be $871.32? Is this correct? Feels like I missed something. Do I have to account for the endorsement?
 
Business math is not an area I excell at. I do have a question before i say your work is fine. Was the $200 owed to the policy holder even if they did not purchase a new policy?? If yes, then your work is off as you do not owe the policy holder a prorated rate for the $200 but rather the whole $200. So in your work above you should have $1,300 not 1,500.
 
Keep in mind that "pro rata" may be defined in the contract. Not all such arrangements use days. Some may do whole months. There are many other possibilities. If we're talking about a practice problem, and not an existing contract, any defensible method may be appropriate. Each coverage must be considered separately.

Also, rounding can be a problem: 1300 * (212/365) = 755.06849315068493150684931506849 ==> 755.07
or 1300 / 365 = 3.5616438356164383561643835616438 ==> 3.56
3.56 * 212 = 754.72
It's only 35¢ different, but this can be significant. Customers can be very sensitive to results that are less than what they are expecting - even if their expectation is based on demonstrably bad calculations.

Point 1: There are mathematical ways and there are practical ways. They don't always overlap.

Point 2: Almost ANY problem, no matter how simple it may seem at first, can lead to a wonderful exploration. Don't miss any opportunity to expand your learning process beyond the narrow focus that may be presented in a book or a classroom.
 
Keep in mind that "pro rata" may be defined in the contract. Not all such arrangements use days. Some may do whole months. There are many other possibilities. If we're talking about a practice problem, and not an existing contract, any defensible method may be appropriate. Each coverage must be considered separately.

Also, rounding can be a problem: 1300 * (212/365) = 755.06849315068493150684931506849 ==> 755.07
or 1300 / 365 = 3.5616438356164383561643835616438 ==> 3.56
3.56 * 212 = 754.72
It's only 35¢ different, but this can be significant. Customers can be very sensitive to results that are less than what they are expecting - even if their expectation is based on demonstrably bad calculations.

Point 1: There are mathematical ways and there are practical ways. They don't always overlap.

Point 2: Almost ANY problem, no matter how simple it may seem at first, can lead to a wonderful exploration. Don't miss any opportunity to expand your learning process beyond the narrow focus that may be presented in a book or a classroom.
Hi, thank you for your reply. So would I indeed subtract the endorsement from the annual premium in this example?
 
Business math is not an area I excell at. I do have a question before i say your work is fine. Was the $200 owed to the policy holder even if they did not purchase a new policy?? If yes, then your work is off as you do not owe the policy holder a prorated rate for the $200 but rather the whole $200. So in your work above you should have $1,300 not 1,500.

Hi, thanks for your reply. The $200 is just an endorsement for something extra. It was fully earned and paid for. Does that answer your question?
 
Hi, thank you for your reply. So would I indeed subtract the endorsement from the annual premium in this example?
That's why I used $1,300 and mentioned that each coverage should be considered separately. Jomo held the same view.
 
That's why I used $1,300 and mentioned that each coverage should be considered separately. Jomo held the same view.

Ok thank you. So do I have to do the same calculation for the $200 and add it to the total, like so:

return premium = 1300 * (212/365) + 200 * (212)/365

Also the 212 represents how many days the homeowner had the policy. Would I need to use 153 days instead, which is how many days remaining on the policy if they would have stayed?
 
Ok thank you. So do I have to do the same calculation for the $200 and add it to the total, like so:

return premium = 1300 * (212/365) + 200 * (212)/365

Also the 212 represents how many days the homeowner had the policy. Would I need to use 153 days instead, which is how many days remaining on the policy if they would have stayed?
you have to use 153 days (unused) for calculating return of premium.

I do not think you have to return any part of the $200, because you had said:

"Part of the premium included an endorsement that was fully earned and paid, that premium was $200 of the $1500"

This statement probably needs legal interpretation first!
 
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