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Math Help - Algebra issue related to Insurance Premium Calc

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    Algebra issue related to Insurance Premium Calc

    Hi All,

    I am stuck with a problem which I feel certain should be solved via algebra, but for the life of me, the soluton evades me. I am interested in calculating a combined insurance premium, where the premium itself is part of the insured amount. I have solved the solution for where there is one cost. I am interested in scaling the formula. The difficulty is probably easier to understand if I put the example into equations:

    C = Cost being insured(known)
    F = Interest Factor to apply to calculate interest on the premium (known)
    R = Premium Rate to apply to calculate the premium (known)
    I = Interest on Premium (to be calculated, but also equal to F.P)
    P = Premium (to be calculated)

    Start point is :
    P = (C + P + I)R ie Premium is equal to the cost being insured + the premium itself + interest charged on that premium with the sum being multiplied by the premium rate.

    We also know that I = F.P (ie the interest factor multiplied by the premium gives the interest on the premium).

    So I rephrased the above as : P = (C + P + F.P)R and solved for P = CR / (1-F.R-R)

    That was all simple and my algebra coped easily and the world was good. However, I am trying to solve something that starts as one level more complex than that, and scales up quite dramaticaly. In this example, I have 2 of everything, 2 costs, 2 interest factors, 2 premium rates and the trick is that I have to insure on both sides the full premium and the interest related to both premium parts. So let's present as follows:

    C1 and C2 = Costs being insured (known)
    F1 and F2 = Interest Factors for each part of the premium (known)
    R1 and R2 = Premium Rates for each constituent part (known)
    I1 and I2 = the interest cost relating to the payment of each premium part.

    My equations are thus the following:
    P = P1 + P2 (Total Premium = Premium on C1 element + Premium on C2 element)
    I1 = F1P1
    I2 = F2P2
    P1 = (C1 + P + I1 + I2)R1 (In both instances the total premium and the corresponding interest charges have to be insured)
    P2 = (C2 + P + I1 + I2)R2

    Now I have presented the P1 and P2 equations as this:
    P1 = (C1 + P1 + P2 + F1P1 + F2P2) R1
    P2 = (C2 + P1 + P2 + F1P1 + F2P2) R2

    I have 2 equations where there are only 2 unknowns (P1 andP2), logic tells me I have to be able to solve this or re-present it to be P1 + P2 (as in total premium) on one side of the equation, but my efforts have gone horribly wrong. Can anyone help?

    The next step would be to consider 3 costs etc...but at this stage I am stuck at this step.

    Many thanks,

    Digit100100

    Sorry, I've been tinkering - taking the original equations:
    P1 = (C1 + P1 + P2 + F1P1 + F2P2) R1
    P2 = (C2 + P1 + P2 + F1P1 + F2P2) R2

    You can rephrase the second equation to be P2 = (C2R2 + P1R2 + F1P1R2)/ (1-R2-F2R2) (which starts to look a little like my original simple equation, which hopefully implies I will eventually get to a scalable answer)

    Now if you substitute the solution for P2 into the P1 equation and manage the algebra, there must be a solution for P1...I just don't know if I am good enough to do it!
    Last edited by Digit100100; April 24th 2010 at 12:35 PM. Reason: Further developed the problem.
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