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Published online by Cambridge University Press: 27 November 2014
It should not be difficult to extend the work already performed by Mr Craig to devise a formula which will be accurate to seven places of decimals even in very unfavourable circumstances (e.g. very long or short terms for very high or low rates of interest). Mr Craig's formula gives the correct value of ρ for the example given in the Textbook, but is not so accurate for more unusual conditions.
Developing as in Mr Craig's note:
We have, as far as terms involving ρ2 in numerator and denominator,
or
and ρ1= t0/t1.
An examination of the form taken by the values of i/ρ — i/ρ1 for various values of n, i and ρ suggests that it is very nearly independent of ρ for intervals up to considerably more than 1/16%.
It would thus probably be possible to find the form of this function from calculated values.