Life Contingencies School Level Maths Proof 1

[Richard Purvey]

Life Contingencies School Level Maths Proof 1

Starting with the two equations:
1. e^(-delta)=v and

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

Method

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

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