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mthly pay life annuity approximation

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  • mthly pay life annuity approximation

    I can derive ax(m)~a(x)-(m-1)/(2m)
    But I cannot derive ax(m)~ax(m)-(m-1)/(2m)-(m^2-1)/(12m^2)(mux+delta)
    The second result uses Woolhouse's summation formula. It is on page 137 of Actuarial Mathematics(1986 edition).
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