LOAN SCHEMES OF lKRTATN RAND FiriLDIXG SOCIETIES. 393 



§5. Bank Ovcrdraii Scheme. — Of seven of the chief 

 societies operating on the Rand wliose schemes here come under 

 review, three (St. Andrews. IVemier. and Goldfields ) g^rant loans 

 on the hank overdraft jn'inciple. Tn the first-named, a loan is 

 granted at 8 per cent. The borrower guarantees a certain mini- 

 mum repayment, btit beyond that tliere is no fixity ; the borrower 

 may repay as nnich of his loan as he likes at any time, and future 

 interest is chargeable only on the uiii)aid balance. This Society 

 makes a feature of tht- fact that " there are no more complicated 

 tables to consult "' ; but one one would think that dispensing with 

 tables is practicable only in a small Society. The other two have 

 regularised the scheme more. .\ loan is granted and is to be 



I 

 repaid in. say, n instalments ; each instalment consists of — -th 



n 

 of the loan together with interest on the un])aid balance, so that 

 the actual sum payable diminishes each month. It is easily shown 

 that for each unit of the loan under this scheme the capital ele- 



I 



ment of the p-\h pax'mcnt made is — . the int^erest element is 



n 



i (1 ), and the total stmi actually paid for the accommo- 



dation is (T -\- I I. As far as total cost is concerned, this 



2 



method is theoretically less onerous to the borrower than an 

 ordinary annuity at the same rate of interest. The total cost of 



111 (I + /)" 



the latter is . 'Yh\^ is alwavs the greater, for the 



(I -f i)'- — 1 

 ditterence between them is 



iii ( 1 -f- Tr- / // -\- ] 



- [ 



( I -f /)" — 1 ^ ^ 



Which may be written 



{u - \)ii ( II -\- I ) i'-' 1 2 3 -j 



^r L _(;,_2)/ -^^ (n-2) ('u-:^)r-^.. 



2 f ( I + / ) " — 1 1 L^ I 4 ' 5 ! 



a quantity which i> essentially j)0<;ifive. 



pjut the j^ractical drawback to the scheme is the comparative 

 largeness of the payments whiclt mtist be made during the early 

 years of the loan. To take an illustrative example, suppose a 

 loan of £ioo is to be repaid bv Ko monthlv instalments, interest 

 being charged at the rate of lo per cent, per annum. Repaying 

 by single-rate annuity t-ach instalment would be £[ 14s. 4'/4^v. 

 an(i the total cost £137 H';. 4d., whereas, on the 



