1822. Mr. Adams on Compound Interest: 451 
will 1 + : = amount of ll. at the end of the rst year. Ii 
like manner, 1 + + 4 + (1 + ~) ats (1 $ ty = amount of 
1d. at the end of the second year. 
(1 + -)° + : (1 + =) = (1 + -)' = amount of 1/. at the 
end of the third year. 
(1 + =) ~ (1 + -)° = (1 + -)* = amount of 1/. at the 
end of the fourth i it 
@eoeeee wpeoeeee eeereeee's ceese Cee eoeoaeres eres esos Hees sree 
Q + ~)" = amount of 1/. at the end of the xth = If the 
last expression be multiplied by the principal P, and + ~=T, we 
shall have P (1 + r)"=s = amount of P ina Vieng ; from 
whence P, r, n, may be found. 
Art. 2.—Tf the payments of interest be supposed to be made 
at m equal gl m a year, then will the interest of 1. for 
one interval be = =, and the number of intervals in n years mn; 
therefore, by writing = for r, and m n for n in the last equation, 
we shall have P (1 = RES x. 
: - we . . , "17 . r 
When P = 1/. and'm infinitely great, then will Q + 5) 
1? n? 13 ns rint 
peer tia gt ea t foe a te 
= a number corresponding to the common log. rn x 43429448, 
&e..- 
Art. 3.—To find the present value of P, due at the end of » 
ears. aa ta cate E 
By continuing the séries in Art 1, downwards; we have 
fee) 
1 + 
( 
(1+ 
( 
amount of 1/, 1 year since, 
= amount of 1/. 2 years’ since, 
) 
ag = amount of I/. 3 years since, 
lh+ ) 
= amount of I/. 4 years since, 
‘1 + +)” = amount of li. n years since. 
The last expression being multiplied by the principal P, and 
262 
