10
ON THE VALUE OF ANNUITIES.
present value of an annuity of £50 for 6 years, at 3^ per cent simple
interest,
1
v 1
== .966184
1 + i
1.035
1
1
= .934579
1 + 2 i
1.07
1
1
= .904977
1+3*
1.105
1
1
= .877193
1 + 4*
1.14
1
1
= .851064
1 + 5 i
1.175
1
1
= .826446
1 + 6 i
1.21
5.360443
50
5 360443 present value of an annuity of £l
\ for 6 years
268.02215 = ditto
£50
To mathematicians, the tables just mentioned will he found of great
use, as they contain the factors, squares, cubes, square roots, cube
roots, and reciprocals of all numbers from 1 to 10,000, with other tables,
and an extensive collection of formulae relating to mathematics and
natural philosophy.
i. e. as
since 1
amount
and prc
n th year
Rule.
same poi
principal
Examj
compound
COMPOUND INTEREST.
19. When the interest of money, instead of being received as it
becomes due, is added to the principal, increasing the sum each year on
which interest is receivable, then money is said to be put out at Com
pound Interest.
If the interest of £100 at ¿£5 per cent, instead of being taken up at
the end of the first year when it becomes due, he added to the principal,
a new principal of ¿£103 is created, which with its interest amounts at
the end of the second year to ¿£110 5, this again forms a new prin
cipal amounting with interest to ¿£115 15 3 at the end of the third
year, and so on for any longer period.
Make s the amount
p — the principal
n — the number of years
i ~ the interest of ¿£l for one year;
then 1 + i — the amount of ¿£l at the end of the first year, and the
amount of any other sum in one year will be in the same proportion,
In this
termed com
(Arithmetic
L °g(l
lo SP
Rules for
the different