454 Mr. Adams on Compound Interest. {Dec. 
L={s0"* = present value of 1. per annum for m years, and 
x oo =< present value of an annuity aforn years. — 
Art. 16.—When n is infinite, [ea will be infinitely small, 
and may, therefore, be neglected, the last expression in that 
case would become = = present value of an annuity a, payable 
yearly for ever. La wt 
Art, 17.—If the interest be payable m equal times in a year, 
1— (i+ ~ ) Mie : 
equation (5) will become ———-——— = present value of 1l. 
( 1+ = -1 
payable every v years, when the interest is payable m equal 
times in a year. ; : 
Art. 18.—If v = 1, and m, as in Art. 17, equation (6) will 
i— aE a 
become i Fes = present value of 1/. per annum for 2 
f+—-— -1 
™ 
years, the interest payable m e ual times in a year. 
" Art. 19.—If an annuity of 1/. per annum be payable wu times 
in a year, then will the expression in Art. 17 become = x 
v-(r4 it)” 
= present yalue ofan annuity of 1/. perannum, 
(: - A —1 
iL 
payable w equal times in ayear, when the interest is payable m 
equal times. (See Art. 12.) 
Art. 20.—When u = m, the last expression will become 
oe (: M 4 agi 
——_—— = present value of an annuity of 1/. per annum, 
when both annuity and interest are payable m equal times in a 
year. 
Art. 21.—When nis infinite, and u = m, — in the last 
05 
1. per annum, when both annuity and interest are payable « 
equal times in a year for ever. (See Art. 16.) 
"Art, 22.—If in Art. 18, n be infinite, then will ————— 
