Life Contingencies School Level Maths Proof 9

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    Richard Purvey
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    Life Contingencies School Level Maths Proof 9

    Starting with the two equations:

    1. 1+i=v^(-1) and

    2. (1+i(m)/m)^m=v^(-1), show that lim v→1 i/i(m)=1.

     

    Method

    Re-arranging equation 1. gives i=v^(-1)-1 and re-arranging equation 2. gives i(m)=m*(v^(-1/m)-1), meaning that lim v→1 i/i(m)=lim v→1 (v^(-1)-1)/(m*(v^(-1/m)-1)), which, after using an Online Limits Calculator, is found to equal 1.

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