made, if upon
mo- in the same
nts of £l per
annuity by the
e nearest quan-
; (by observing
ximation to the
in 10 years to
aum in 10 years :
e amounts of £l
035
.03
. 005<
difference
of interest.
1.375425
276 — 11.6035
suit is very near
cent: if .03263
; then have ob-
= .03263, and
r cent the propor-
ntly near for most
rte.
nd interest is con-
mmber of periods
two payments of
a year is therefore
COMPOUND INTEREST. 37
and the following series is therefore the amount of an annuity of ¿£'1
at the expiration of n years, since each payment is
H I+ ( l+ iy + 0 + i)-'+0 + ij z + ••••
+ 1 + -
7 \ m (. mn — 2 )
r
+ ( 1 +
Substituting, as in Art. 44, we have here 1 = the first term, min —
the number of terms, and ( 1 + — ) m ' = the common ratio, and the
\ m )
sum of the series will be
/, i\ mn
i 0 + -) -
\ mj
(l + - 1
\ m/
1 +
m
- 1
when m — in' then — — 1, and the formula becomes
a ( l + =) - 1
a l 1 +
<6 \ on
( 1 + ^) - 1
What will an annuity of £20 amount to in 12 years at 6 per cent
compound interest, when annuity and interest are payable half-yearly?