The recent paper by Dr Hagstroem (J.I.A. Vol. LXX, p. 119) directs attention to the very closely related subject of the effect on life assurance premiums of changes in the rate of interest. Some four years ago, in the course of an address before the American Life Convention, Mr V. R. Smith studied the relationship of the interest rate to life assurance premiums from a different angle. This note is an attempt to develop the mathematical theory underlying Mr Smith's method and to present some results on the basis of the A 1924–29 Table.