Annuities Treated without Progressions

Extract

The method usually given in text books on Algebra for finding the present value of an annuity to last for a given number of years, or the accumulated amount of an annuity left unpaid for a given time, consists in writing down the present values or amounts of the several payments, and summing them by the usual formula for a geometrical progression. The following method, by which the result is found from first principles without the use of formulae, is so simple and instructive that I am rather surprised that the idea does not appear to have suggested itself to teachers and writers of text books before now, or, if it has done so, that it has received so little notice.