My Math Forum How to divide insurance payout fairly

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May 21st, 2012, 04:39 PM   #11
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Re: How to divide insurance payout fairly

Thank you for your input. I have attached the actual figure as someone else may be interested. I am not sure if FV (future value) calculation would miss something that needs to be taken into consideration? Please help.
Attached Files
 ins_1_n1.xls (27.5 KB, 31 views)

 May 21st, 2012, 07:45 PM #12 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Re: How to divide insurance payout fairly Can't open that file...
 May 21st, 2012, 11:23 PM #13 Senior Member   Joined: Apr 2011 From: USA Posts: 782 Thanks: 1 Re: How to divide insurance payout fairly I can open the file but there's much about it I don't understand. There's dividends, but I don't know if those are individual amounts or some cumulative total, and you hid column D. I don't understand what columns F & G are. I don't know why they keep getting bigger, and it's not because it's being added to the prior one, cause that's what columns H & I are doing. I don't know what the cash value means, but maybe not anything for your purposes. Since E, F & G keep getting bigger, there may be some growth already built into them, but it's nothing steady. I wouldn't want to say a word about any of that without knowing what it means. Again, I'd just have to repeat that I think you need to know more about how insurance actually works. Seeing numbers doesn't tell me what they're doing. I don't know where some of it came from. You've got equations in that bottom section based on numbers I don't see. I don't know what the face value means, cause it's less than the total PUA's (whatever that means), and I don't know where on earth you got that interest rate. I don't even know what the actual payout is. If the basic payout is JUST based on the payments made, you can do what Denis showed you, which is what you seemed to have started out doing on your own anyway, except using an unrealistic interest rate. But I don't know how any of the rest of it works.
May 22nd, 2012, 07:24 AM   #14
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Re: How to divide insurance payout fairly

Thank for input. [attachment=0:15lfy08h]insur_1.xls[/attachment:15lfy08h]
1. Insurance company invested yearly premium received into shares, bonds, other financial products to get capital growth as well as income in terms of dividends, interests, etc. In our case the dividends received were invested/used to buy more shares, bonds, financial products as shown in column F/G. Column H/I total pua (paid up addition = bonus additions) was the sum of Bonus (F or G year(t-1)) + Bonus (F or G (year (t)).
2. Column J/K Cash value is the amount you'll get if you surrendered the policy/stopped payment at a particular year. However, you'll get the insured amount $25,000 if accident happened. 3. A or B only contributed 25% of the premium, whereas C contributed 75% of the premium. Hope it would make it clearer now. Attached Files  insur_1.xls (25.5 KB, 31 views)  May 23rd, 2012, 07:15 AM #15 Member Joined: May 2012 From: Sydney Australia Posts: 30 Thanks: 0 Re: How to divide insurance payout fairly Thank for your input/opinion. (Refer to insure_1_n1) I applied Excel FV(future value) formula and interpolation to find the interest rate X (see my prior post) by trial and error using 11% ie FV(0.11,22,-348.25,0,1)=31,394.00;12% ie. FV(0.12,22,-348.25,0,1)=36,079.71; X% ie FV(x,22,-348.25,0,1)=35,913.33; So (x-0.11)/(0.12-0.11)=(35913.33-31394)/(36079.71-31394). Hence x=0.11964492 (11.96%). In this formula I used the total settlement amount including the insured amount$25,000. The insured amount $25,000 is only payable when accident happened. It is just like winning a lottery. So, should I exclude it in my initial FV equation, and only after I got Mr A and Mr B share of the rest of the insurance settlement, the$25,000 got apportioned accordingly? Please help. Thank you. Regards thirst4answer.
 May 23rd, 2012, 10:42 AM #16 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Re: How to divide insurance payout fairly Still can't reach your attachment; I can confirm that 11.96% is correct for: PMT=-348.25, N=22, FV=35913 ; (beginning of period payments) Your question on the $25,000 seems to require a legal decision. Anyway, 35913 - 25000 - 348*22 = ~3260, which is the net "earnings". Seems a minor amount to try and calculate to the last penny; why don't A and B flip a coin for it? If it was up to me (as the Ins. Co. accountant) I'd send a cheque for$35,913 payable JOINTLY to both (Pay to the order of Art and Ben!) and let them work it out...since they both need to endorse cheque, than that would constitute their acceptance of the breakdown...
 May 23rd, 2012, 11:03 PM #17 Senior Member   Joined: Apr 2011 From: USA Posts: 782 Thanks: 1 Re: How to divide insurance payout fairly You really could have made this much easier by explaining all this up front. (I'm still wondering if there's more surprises.) Are you saying if there weren't an accident they'd only get the 10,913.33?? Since I don't know how insurance is "supposed" to work, this is all only my opinion, based on my understanding, and I can't guarantee that I'm understanding it correctly. A FV of an annuity includes the payments. Your 10,913.33 does not - that's the earnings on it only. A true FV would be 10,913.33 PLUS the 348.25*22. Which is 18,574.83. (Although I'm still not comfortable with what "paid up additions" means, simply cause it suddenly starts growing awfully fast.) If they only got the additions, they're getting earnings, but not what they actually put into it, or 3252 earnings as Denis pointed out. Which is 2.97% earnings on the payments they put in, which isn't very good. If they aren't getting the $25,000 then no, I don't think you should be including that in when calculating the interest rate. If they don't get it, it seems to have nothing to do with anything. I think getting earnings only is a funny way of doing things and it makes it more difficult to think about (just cause I'm not used to it). But if they're getting 10,913.33, then I would use that number only. And since all those "additions" have come directly from their payments, or reinvestments of earnings, as far as I'm concerned that's already built into it. And then personally, I would use that interest rate (2.97%) and figure out the FV of just A's payments, which is 4798.50. B gets the rest. And it's only fair A get a higher share than just the payments put in, cause A started sooner and tied it up longer.  May 24th, 2012, 10:37 PM #18 Member Joined: May 2012 From: Sydney Australia Posts: 30 Thanks: 0 Re: How to divide insurance payout fairly Thank you 4 ur input. I have provided the fv calculation below for compound interest that X paid$100 for 2 years, then paid $40 for next 3 years while Y started the payment$60 on year 3 to year 5. yr o/bal x y int 12% c/s bal 1 100 100 0 12 112 2 112 100 0 25.44 237.44 3 237.44 40 60 40.4928 377.9328 4 377.9328 40 60 57.351936 535.284736 5 535.284736 40 60 76.23416832 711.5189043 $100$100 $40 first 2 yrs next 3 yrs 3 years total x=$237.44 333.5861043 $151.17$484.76 y= $226.76$226.76 \$711.52
May 24th, 2012, 10:58 PM   #19
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Re: How to divide insurance payout fairly

Thank you 4 inputs. I have attached pdf file as the prior posting did not line up properly. I hope it'll help as I got difficulty in posting excel spreadsheet.[attachment=0:97oycjln]Math_ex_1.pdf[/attachment:97oycjln]. I can only attache one file. Can you help me how to attache 2 files?
I'll attach pdf/doc format of my previous excel spreadsheet to help understanding the case easiler.
Attached Files
 Math_ex_1.pdf (73.0 KB, 43 views)

May 24th, 2012, 11:08 PM   #20
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Re: How to divide insurance payout fairly

Attached Files
 ins_excel_1.pdf (73.8 KB, 47 views)

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