II. The yield on an annuity or a loan

Extract

The problem considered is that of Todhunter's Textbook (1936 edition), ch. VIII, para. 6, p. 176, but the method employed is suitable also for finding the yield on a loan issued at a price different from par, and redeemable through the operation of a cumulative sinking fund, applied in drawings at par or at a premium.

Let a′ be the value of an annuity of 1 payable annually for n years; it is required to find i′ the unknown rate of interest.

An examination of any published set of tables of annuity values, such as Oakes's Tables, will indicate that rate of interest i, to the nearest ⅛ %, at which is most nearly equal to a′.

Let dashed symbols refer to functions calculated at rate of interest i′.