6 
ON THE VALUE OF ANNUITIES. 
s denoting the sum of the series, n the number of terms, a the first term, 
and h the common difference ; applying this to the above series we have 
n terms in both, a = 1, b — i; the sum therefore is expressed by the 
formula 
n (2 + (n — 1) 0 n (n — 1) i 
_ n + g > 
and this multiplied by a gives 
s — a (71 + ^ n—~ 0 = the amount of an annuity of £a in 
A 
n years. 
Rule. Multiply the number of years by the number of years less 
one, and by the interest of £l for one year; to the half of this product 
add the number of years, and multiply the sum by the annuity. 
Example. What is the amount of an annuity of £325 forborne 12 
years, at 3^ per cent simple interest ? 
n ~ 12 o = 325 i — .035 
n — 1 — 11 
n (n — 1)— "132 
i - .035 
660 
396 
2)4.620 
n + 
n.(n — l).z_ 
2 
n ~ 12 
l).i ~ 
= 2.310 
n, (n 
= 14.310 
a = 325 
71550 
28620 
42930 
a \ n + - 
n. (n —1) i 
= 4650.750 = ¿£4650 15 0 the amount. 
15. To find (a) the annuity, the amount, &c. being given, 
(Art. 14.) 
s •sz a ( n + 
n (w — 1) 
multiply each side of the equation by 2, then 
2 s = a (2 n + n (n — 1). i) 
dividing each side by 2n + n (n — l).iwe have 
_ 2_s 
2n + n (n — 1) i‘ 
Ride. Multiply the number of years by the number of years less 
one, and by the interest of £l for one year; to this product add twice