LOAN SCHEMES OF CKKTAIN RAND BUILDINO SOfJKTIKS. 395 



capital element of the first instalment, C\. that of tlie p-lh is 

 Cj ( I -f /)^"\ which may be written 



p-l . p-2 



C\{1 + p-i . i -\ . r + . . . -h i I"-') 



2 ! 



Hence if we were to neglect second and higher powers of /, 

 we should obtain cai)ital elements increasing uniformly. 



Ci ( I + /' - I • ; ^"^ ^^^^ neglect leads to serious error, espe- 

 cially in the longer period tables. The consequences of this un- 

 sound method of construction of the rej^ayment schedules are far- 

 reaching; the following extract shows that, according to the 

 Society's own figures it expects to earn up to 170 per cent, on 

 the loan outstanding towards the close of the transaction. 



'fe 



Eight Years' Table. 



Interest Rate 



Months Redemption Value I'Jement in Instal- per cent. 

 run. during this month. ment just paid. per amnnn. 



£ s. d. s. d. 



72 32 13 10 5 9 TO. 6 



84 17 10 II 3 II 13.4 



96 I 6 5 3 g 170 



Comparison of these wnth the correct values given below 

 shows that the outstanding debts, and conse(|uently the assets 

 of the Society, are consistently undervalued : — 



Interest Rate 



Months Redemption Value l^lement in Instal- ])ercent. 

 run. during this month. ment just paid. ])er amnnn. 



^£ s. d. s. d. 



72 34 ^ 4 3 '"^ TO 



84 18 12 3 3 I TO 



96 1 K> I o 3 10 



And we see how the neglect of s(|ua'-es and higher i)owers 

 leads to cunmlative errors which make their presence felt 

 towards the end of the teruL 



Perhaps the most interesting result to which this basis of 

 calculation leads is the following gem extracted from this 

 Society's five years table : — 



MoNTin- Jnstalmknt. £2 2s. 6d. 

 Months run. Kedemption Value. 



59 2 3 1 



60 o o o 



