

An annuity of i jttn deferred for t yean ii now worth 



,1 l 



A perpetuity deferred for * years is worth - orr*p; but a perpe- 

 tuity due in k yean is the same as a perpetuity deferred for i- 1 

 yean, and k I must be written for i- in the preceding ; giving 

 **- ' p. 



If the proceeds of an annuity of n yean be put out to interest as 

 fact as they become due, then at the instant after the last payment is 

 made the first payment will have improved for n 1 years, the second 

 for n 2 yean. 4c., and the last payment will have made nothing : 

 whence the whole amount of the annuity at the moment of expira- 

 tion is 



. . . . (! + ) -1 1-g" 



which is or 



r n 



The annuity of H years, which It will buy, makes at each payment 

 -:- ( 1 t" ) ; and so on : that is, the following are methods of re- 

 storing It now lent : 



1. By annuity for * yean . . . . 



t. By annuity for yean, deferred ft yean, of 



3. By perpetuity of 



4. By perpetuity deferred for I yean . . of 



And It due at the end of yean, may be paid by an K yean annuity 

 of '-!- (1 ), or by an annuity due of IT* -=- (1 + r ). 



It is hardly necessary to say, that an annuity, to., of i U to be 

 found by multiplying the annuity, tc., of It by i, 



An annuity of n years, which gives It at the first payment, 2t at 

 the second payment, Ac., and Jin at the nth and last paynv 

 worth 



(I-")* 



and when the numerator and denominator change places, we have 

 the fraction of It, which must be paid at the end of the first year, in 

 order to repay It now lent, by uniformly increasing instalments in n 

 f 

 An annuity of n yean, which gives n at the first payment, (n 1) 



TIBLX III. 

 Tn Ajtxrrrr WHICH 1 WILL rvicnur ro* ANT JUMBKS or TEABH. 



TADI.E IT. 

 THB AJIOVST or 1 IK AXY M-VBIR or Tula. 



