ANN 
ANN 
dyeing wax of a Vermillion colour. Wool 
and silk, boiled in a solution of it by alka- 
line salts in water, acquire a deep, but not 
a durable orange dye ; for though it is not 
changed by alum or acids, it is discharged 
by soaps, and destroyed by exposure to the 
air. It is said to be an antidote to the poi- 
sonous juice of manihot, or cassada. The 
liquid sold under the name of “ Scott’s nan- 
keen dye,” seems to be nothing but annotto 
dissolved in alkaline ley, 
ANNOYANCE, in law, any injury done 
to a public place, as a high-way, bridge, or 
common river ; or to a private way, as lay- 
ing any thing that may breed infection, by 
encroaching, &c. 
ANNUAL plants, generally called an- 
nuals, in gardening, signify such plants as 
are of one year’s duration, or which conti- 
nue for a few months only. Plants that rise 
from seed sown in the spring, arrive at ma- 
turity in the summer or autumn following, 
producing flowers and ripe seed, and which 
afterwards perish in their tops and roots, are 
commonly regarded as annuals. The plants 
of this tribe are very numerous, as most of 
those of the herbaceous kinds, consisting of 
uncultivated plants, weeds, &c. and also a 
great number of cultivated garden and field 
plants, both of the esculent and flowery or- 
namental kinds, are of this description. 
The last sort are often termed simply an- 
nuals. These are divided into the hardy 
and tender kinds ; the former are sown in 
places where they are designed to remain 
without transplanting, but the latter are 
usually sown in hot-beds, in order to be 
transplanted in the spring, either into pots 
or borders. 
ANNUITIES, any income of a certain 
yearly amount, payable at particular periods, 
which may be either yearly, half-yearly, 
quarterly, monthly, weekly, or at any other 
intervals. They are usually distinguished 
into annuities certain, and contingent an- 
nuities, or such as are for an uncertain pe- 
riod, being determinable by some future 
event, such as the failure of a life or lives. 
The present value of an annuity is that 
sum which, if improved at compound in- 
terest, would be sufficient to pay the an- 
nuity : the present value of an annuity cer- 
tain, payable yearly, and of which the first 
payment is to be made at the end of a year, 
may therefore be calculated in the following 
manner. 
Suppose a person has 1001. due to him a 
twelvemonth hence, and he wishes to have 
the value of the same advanced immediately 
VOL. I. 
the sum which ought to be given as an equi- 
valent thereto, allowing 5 per cent, interest, 
is 95 1. 4s. 9 \d. for this is the sum which, 
put out to interest at the rate of 5 per cent, 
will, at the end of (he year, amount to 1001. 
So also, if a person has 1001. due to him at 
the end of two years, and he wishes to have 
the value of the same advanced immediately, 
the sum which ought to be given as an equi- 
valent thereto is 901. 14s. 0 |cl. for this is the 
sum which, put out at the same rate of in- 
terest, will, at the end of two years, amount 
to 1001. In like manner, if a person has 
1001. due to him at the end of three years, 
and he wishes to have the same advanced 
immediately, the sum which ought to be 
given as an equivalent thereto is 861. 7s. 8 d. 
for this is the sum which, at the same rate of 
interest, will at the end of three years amount 
to 1001. And if these three values are ad- 
ded together, they will make 2721. 6s. 6d. 
being the sum which ought to be paid down 
for an annuity of 1001. for three years ; as 
this sum improved at the given rate of in- 
terest is just sufficient to make the three 
yearly payments. 
As the amount or present worth of 11. for 
any given term is usually adopted as the foun- 
dation of calculations relating to annuities ; 
let r represent the amount of 11. in one 
year; that is, one pound increased by a 
year’s interest, then ?■», or r raised to the 
power whose exponent is any given number 
of years, will be the amount of 11. in those 
years; its increase in the same time is 
r n i . n ow the interest for a single year, or 
the annuity corresponding with the in- 
crease, is i — 1 ; therefore, as r— 1 is to 
r n i go is u (any given annuity) to a its 
amount : hence we have 
v x t" — l 
r — 1 
Example. — To what sum will an annuity 
of 501. amount in 6 years, at 5 per cent, per 
annum compound interest ? 
50 x I'-Oa’- 6-1 —340 1. 19s. Id. 
.05 
In this manner the amount of an annuity 
for any number of years, at any given rate 
of interest, may be found. But when the 
term of years is considerable, it will be 
more convenient to work by logarithms, by 
which the labour of all calculations relating 
to compound interest is greatly abridged. 
There is, however, little occasion in general 
to calculate the amount or presen! worth of 
annuities, except for particular rates of in- 
terest, as the following tables, and others of 
R 
