39- LOAN SCHEMES OF CERTAIN RANn lU'ILDING SOCll'.TIES. 



is just the same as if the capital debt had remained unaltered and 

 the sinking fund, /, had been invested at the rate / for the period. 

 The capital element contained in the /i-th instalment is 

 / ( I -j- i) f''^ ; when that instalment has been paid the total 

 reduction of capital ( or the accumulated value of the sinking 



( I + /,)^ -I 

 fund) is — . and consequent!}- the redem])tion value, 



fi + /)" -I 

 that is, the balance reniaining- unpaid at that stage is 



(i+i)"-(i+ /■)■" 



. To a Building Society whose members have 



(i+i)« -I 



the right of redemption al any time, it is of importance that 

 redemption schedules should be constructed for each of its loan 

 tables, giving such an analysis of each repayment into its interest- 

 and capital-elements ; for the assets of such a Society, in so far 

 as its loans on mortgage are concerned, consist of the unpaid 

 balances thus determined ; the profits during any period consist 

 of the sum of the interest elements of all repayments made 

 during that period, and, where such concerns are subject to 

 income-tax, only the interest elements of the various repayments 

 are taxable. 



§3. All Building Societies operating on the Rand charge 

 interest on their loans at a rate higher than any they could hope 

 to obtain with safety from other investments. If, then, the 

 sinking fund is not invested in the security of the debt itself, as 

 is the case when each capital element is directly applied to the 

 redtiction of the loan, they are comj^elled to let it accumulate at 

 a lower rate. In this case the annuity ])ayments must be fixed 

 so that the Society realises the higher (remunerative) rate on 

 the loan during the whole term, while the sinking fund accumu- 

 lates at the lower (reproductive, or accumulative) rate. This 

 scheme is naturally less advantageous to the borrower than a 

 single rate annuity at the same higher rate, for, not only has he 

 to pay the higher rate on the unpaid balance, but he nuist also, 

 during the whole currency of the loan, bring u]) to the higher 

 rate the interest being earned by the sinking fund accumulating 

 in the hands of the lender. When, however, the remunerative rate 

 in a double rate annuity is less than that charged under a single 

 rate scheme, a special calculation is needed to ascertain Avith 

 which the advan.tage to the borrower lies. 



§4. Rand Building Societies may be criticised from two 

 points of view. In the first place an examination may be made 

 of the soundness or otherwise of the attempts made at putting 

 into practice recognised princi])les in tlie theory of finance — a 

 startling commentary upon financial life in Johannesburg that 

 such criticism is needed; and, secondly, an examination may be 

 made of the terms offered to the borrower under the different 

 schemes. 



