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By Guy E. Churchill, R Brown, G. Chandler and W. A. Davis (Auth.)

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The present value, at an effective rate of interest of 6% per annum, of a special annuity-certain under which payments of 1 are made at the beginning of the first, third, fifth, seventh and ninth years, is 4-014. Find the value of ajöi at an effective rate of interest of 6% per annum.

0-05; it follows that half of this is 6d. = £0-025, and halving this again: 3d. = £0-0125. Memorize these before passing on. SELF-TEST Write down as decimals of £1 ; 4s. ; 18s. ; Us. ; 8s. ; 10s. ; 10s. 9d. CHAPTER 4 Annuities in Advance Now WE come to another peculiarity of terminology; an annuity payable in advance is called an annuity-due, even though it is not due (in the outstanding sense of the word) for very long— perhaps a day or two at the most—because it is paid immediately (really immediately).

A. for ever is 1/f, which = a^\. Now the value of anything deferred or delayed by d years is d v times its value if it were not delayed. a. , d or in symbols: d\a^ = v ji and we have just independently established that = 1 //. DEFERRED PERPETUEES 49 Now what do these two values differ by? is more than \a^\, but by how much? They differ by the present value of the first d year's payments; these are included in α—| but they are excluded from d\a—\. After the first d years, the two sets of payments do not differ at all; they both go on for ever.

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