On the Rate of Interest in Annuities-Certain

Extract

The problem of finding the rate of interest corresponding to a given annuity-value, has engaged considerable attention at various times; and many formulas have been proposed for obtaining approximate solutions by the aid of existing tables of annuities. Most of these will be found in Mr. Sutton's paper on the Rate of Interest yielded by Foreign Loans (J.I.A., xix, 77). Of the 5 formulas there given, (2) is probably the most generally useful, (3), (4), and especially (5) (Prof. De Morgan's formula), involving a good deal of calculation. The object of the present short paper is to suggest 2 new formulas, which give very accurate results, and at the same time require but little work in their practical application.

Let a be the value of an annuity for n years certain, at a rate of interest i, (which it is required to find), and let a₁, a₂, a₃, be the tabulated annuity-values for the same term at the rates i₁, i₁ + h, i₁ + 2h, where a lies between a₁ and a₂, and consequently i between i₁ and i₁ + h.