394 L<->AN SCIIKMKS uy li'.KTAlX KAXD i;UILDIN(; SOCIKTIES. 



fixed capital-reduction scheme tlie first instalment should 

 be £2 IS. 8<i.. the last £1 5^. 3d., and the total cost 

 only £133 15s. But the early years of the loan have to bear the 

 greater share of the burden, and as they are tisually the lean 

 years, the scheme might be o})en to objection on that account. 

 Objection must be taken, also, from another point of view, to 

 some of the methods adopted to put the scheme into operation. 

 Here, for instance, is one of the tables: — 



I ()A.\ Tai:! K 15 



Class IJ. — £100 repayable in So Monthly I fiiiiiiiishiiu/ Faynwiits 

 at 6 per ccnlA !) Interest as /o/Zo^cor : — 



.Subscriptions. 



Althotigh the capital is being reducefl monthly, the interest 

 payable is constant during each year ; the borrower is therefore 

 de])rived of the interest on his sinking fund during each year, 

 and gains no financial credit whatever for the monthly redtictions 

 of his loan. Moreover, the interest is stated to be 6 per cent. 

 On the contrary, the rate is 10V2 per cent at the beginning of 

 each year, and, owing to the non-crediting of interest to the sink- 

 ing fund, the rate rises to 121/' pc cent, at tb.e end of each year. 



§6. Single-rate Aiitorllsatiuii. — The single-rate annuity 

 scheme is favotired by three Societies — the Rand Provident, the 

 Alliance (which has also a double-rate scheme), and the United. 

 The interest charged is nonfinally 10 per cent. ])er annum. Oi 

 these Societies, the repayment schedtiles of the first-named are 

 nearly, but not qttite, accurate, those of the second are not dis- 

 closed in its prospectus, while those of the third are constructed 

 on a peculiar and unsound basis which may rc])ay more detailed 

 consideration. 



In §2 it was shown that the capital element contained in 



the p-\h payment of such an aniun'ty is x' per unit 



•=*^(i 4- /)"— I 



of the loan; hence the capital elements contained in successive 

 repayments form a geometrical series. In tb.e repayment .sched- 

 ules published by the United Building Society, on the other hand, 

 these elements form as nearly as [possible an arithmetical series. 

 This, as a matter of fact, does give an a|)i)roximation to the 

 correct value for the shorter period schemes ; for, calling the 



