Lesson
4:
Annuities:
Future
Value
Part
A

Definitions/Introduction
Annuity:
a
series
of
equal
payments
or
investments
made
at
regular
intervals
of
time
:
Simple
annuity:
an
annuity
in
which
the
payments
coincide
with
the
compounding
period
Ordinary
annuity:
an
annuity
in
which
the
payments
are
made
at
the
end
of
each
interval
Note:
We
will
deal
with
simple,
ordinary
annuities.
Part
B
—
Deriving
the
Formula
Chie
has
decided
to
save
$1
000
each
year
from
her
parttime
job.
She
does
this
for
5
years
and
invests
the
amount
each
year
at
9%/a
compounded
annually.
How
much
will
she
have
saved
at
the
end
of
the
5%
year.
Draw
a
time
line.
Now
1
year
2
years
3
years
4years
5
years
f
f
f
f
t
i
deposit
deposit
deposit
deposit
deposit
$1
000
$1
000
$1
000
$1
000
$1
000
As
=1000
9%
compounded
annually
A,
=1000(1.09)
A;
=1000(1.09)?
A,
=1000(1.09)°
A,
=1000(1.09)*
At
the
end
of
the
5%
year,
the
amount
of
money,
including
interest,
accumulated
is
given
by:
S5
=1000
+1000(1.09)
+1000(1
.09)2
+1000(1
.09)3
+1000(1
.09)4
——p
—a+ar+ar®+ar®+ar®
a(r"
—1)
This
series
is.a
geometric
series
and
the
formula
S,,
=
can
be
used.
Therefore,
1000
(1.09°
—1)
°
1.091
=
5984