SIMPLE INTEREST. 
9 
Arith. and Alg., 109. By transposition 
dividing each side by n (n — 1) 
• = 2 (t ~ ") 
n (?i — 1) 
Rule. Divide the amount by the annuity, subtract the number of 
years from the quotient, and multiply the difference by 2; then divide 
by the product of the number of years, multiplied by the number less 
one. 
Example. At what rate per cent simple interest will an annuity of 
£325 amount in 12 years to £4650 15 0? 
s = 4650.75 a ~ 325 n = 12 
325)4650.75 ( 14.31 
325 12. 
1400 - —w=2.31 
a 
1300 2 
1007 4.62 
975 • 
325 
325 
18. If we wish to obtain the present value of an annuity, it can be 
done by finding the present value of each payment separately, and the 
sum of these several values will be the present value of the annuity. 
If we suppose the annuity to be £l per annum for n years, the ex 
pression for the present value will be by Art, 6, 
1111^ 
1 + * 1 + 2i 1 + 3z T 1 + 4i T 
1 1 1 
1 + (n — 2) i 1 + (n — l)i + 1 + in 
For the summation of this series no general formula has yet been dis 
covered, and when the annuity whose present value is to be found, is for 
a long term of years,, the computation becomes tedious; it may, how 
ever, in most cases, be considerably abridged by the assistance of Bar 
low's Mathematical Tables, in which are given the reciprocals of all 
numbers from 1 to 10,000; for instance, if it were required to find the 
12 = n 
11 = n — 1 
n {n - 1) =132 4.62(.035x100 
396 = 3.5 percent. 
660 
660