396 LOAN SCHEMES OF CERTAIN Ra.xd r.U ILDI X( , S( K IF.TIKS. 



With one month still to run the debt amounts to £2 3s. id., 

 at the end of the month it is only £2 2s. 6d. It is surely a new 

 theory in financial practice that a debt grows smaller as it grows 

 older. 



§7. Doitble-rate Ainortisalion. — Two Societies — the Alliance 

 and the S.A. Permanent Mutual — offer a double rate annuity 

 scheme. In its prospectus the former does not disclose the 

 remunerative rate, while its reproductive rate varies with the 

 profits earned. Tlie latter's scheme is clear and well-defined. 

 The renumerative rate is 8 per cent, per annum, payable in 

 monthly instalments ; a reproductive rate of 5 per cent, per annum 

 is guaranteed for the sinking fund, and to this is added extra 

 profit, which has hitherto averaged 2 per cent. This scheme is 

 reasonable and straightforward in its operation, and. as we shall 

 see just now, it is more advantageous to the borrower than the 

 ordinar}' 10 per cent, amortisation, even if the extra profit is only 

 I per cent. 



§8. Comparison of Benefits. — Having once settled which 

 Societies are able to operate their schemes correctly, the bor- 

 rower next incjuires which scheme will offer him the least oner- 

 ous terms. A common monthly payment seems to be the most 

 satisfactory basis of comparison ; for this ])ayment we shall 

 take the instalment jiayable in the case of the ordinary single-rate 



n ' <^ + ^^" 



annuity, which amounts to 4- per unit of the loan. 



**^(i -f /■)"-— I 



Now if a payment a is made 77; times a year in amortisation of a 

 loan on which interest is charged at the rate of t'/, pet' i per 

 annum, likewise ])ayable in ;// instalments, the sinking fund 

 accumulating at £/. per £ per annum, the accumulated value of 

 the sinking fund at the end of // years is 



I -f ;V' - 1 



h 



III 



y. 



— . Ill - I ) 



h I" 2 



This result is used in the calculation of the figures given below. 

 The first column gives the number of years during which pay- 

 ments are to be made; tlie second, the monthly payment made; 

 and the other columns contain tlie sums to which those pavments 

 would amount under the different schemes, at the termination 

 of the annuity. 



