In Pension Fund work there arises the problem of determining the cost of a pension dependent upon salary and length of service, and it is often required to ascertain how this cost would be affected if a different salary scale were substituted for that upon the basis of which calculations have already been made. Attention will be confined in this Note to the type of scale most common in practice, namely, the ‘ratio’ scale wherein the successive values form a series of proportional numbers showing the average ratios by which present salaries may be expected to increase from age to age in the future.

We will suppose that the contribution, expressed as ą percentage of salary, is required on one scale when it has been calculated on another scale, or that the various effects of using several possible scales are to be determined. It may happen that the nature of the scales, or to be more precise their relative nature, is such that in order to find a solution to this problem we must consider the effect of the change separately upon the value of the pension benefit and upon the value of a contribution of 1 % of salary; or it may even be necessary to recalculate the required figure on each of the different bases.