23J 
«T INTEREST AND A N XU I TIES. 
The use of which theorems, respecting the present 
values of annuities, as well as of the preceding ones* 
for compound interest and annuities in arrear, willfully 
appear from the following examples. 
Examp. 1. To find the amount of ¿75/.in seven years; 
at lour per cent, per annum, compound interest. 
In this case we have given P — 575, 11 = 1,04, and 
n — 7; therefore, bp Theorem 1, log. a xx log. 575 + 
7 log. 1,04 = 2,8789011; and consequently a — 
756,66, or 756/. 135. 2-fd. the value required. 
Examp. 2. What principal, put to interest, will raise 
a stock of 1000/. in fifteen years, at 5 per cent. f 
Here we have given R — 1.05, n r 15, and a — 
1000; therefore, by Theorem 2, log. P = log. 1000— is 
log. 1,05 — 2,6621605; and consequently P — 481,02 
•or 481 /. 05. 4ii/. the value sought. 
Examp. 3. In how long time will 575/. raise a .stock 
of 756/. 135. L 2?d. at 4 per cent. ? 
In this case we have R = 1,04, P =: 575, and a xz 
756,66; whence, by Thcor. — 1^2! 
xz 7 e the number of years required. 
56,66 — log. ¿75 
fog» 1,04 
Examp. 4. To find at what rate of interest 481/. in 
fifteen years, will raise a stock of 1000/. 
Here we have given P =: 481, a zx looo, and «=: IS; 
therefore, by Theorem 3, log. it — \ 000 _ 
] 5 
— .0211903, whence R rr 1,05; consequently 5 pet 
cent, is tne rate required. 
The four last examples relate to the cases in com 
pound interest ; the four next are upon the forbearance 
of annuities. ' 
Examp. 1. If 50/. yearly rent, or annuity be forborne 
seven years, what will it amount to, at 4 per cent per 
annum, compound interest. 
Here we have R — 1,04, A — 50, and n — 7; and