‘ (1+7)° —1 
—  ————————EEeEeE—eEEeEeEeEeEeEeEeeeeEOOeEeEeEeEeEeE=EmEmomomauaaPEEeEeEeEeEeeeEeEeEeEeEeEeEOOEeEeeeee ee 
1822.] ‘Mr. Adams on Compound Interest. 453 
Art. 10.—If the interest be payable m equal times in each 
mn 
(1+2 -1 
m™m 
(1+ 2 eee 
™ 
payable every v years, when the interest is payable m equal 
times in a year. 
Art. 11.—If v = 1, and m, as in Art. 10, pio (a) will 
(1+ zy ions 1 
(is, Ly a 
a the interest is payable m equal times in a year. 
Art. 12.—If P instead of representing a multiple of whole 
year, equation (2) will become = amount of 1/. 
= amount of an annuity of 1/. per annum, 
henaae 
years, represent “th part of a year, then will the expression in 
ug 
(+2 
1/. per annum, payable wu equal times ina year, when the inte- 
rest is rs. m equal umes; z will represent the annuity at 
Art. 10 become ~ x 
= amount of an annuity of 
first, or the ~ th part of the yearly annuity. 
Art. 13. To find the present value of 11. payable every v years 
during ” years, the interest payable yearly.. 
By Art. 3, 
oa. = present value of 1/. at the end of the first period, 
a = present value of 1/. at the end of the second period, » 
— = present value of 1/. at the end of the third period, 
Tear = present value of 1/. at the end of the v periods, 
1 1 1 
therefore, isn at wet tare aa thubus speeder ee 
1 —(l+r)-"” 
_(l+r-—1 
tee teste te caccreccseresswoceceeres sere) 
Art. 14.—When 7 is infinite, the last expression becomes 
1 
= present value of 1/. payable every v years, during 
= present value of a perpetuity of all such fines. For 
in that case (1 + r)~" would become infinitely small. 
Art. 15.—When v = 1, the expression (6) will become 
