33 Part I
Annuities
Ordinary annuity
a sequence of equal periodic payments
made at the
end
of each payment period
Example: an annuity of 4 payments of $100 per month
Question
: How much is the annuity worth (its
future value
) at
the end of 4 months?
Assume payments are being placed into a
savings account at 12%.
We use the following symbols:
PMT = the periodic payment
i
= interest rate per period
n
= number of payments
FV = amount (
future value
of the annuity)
The general formula is:
FV = PMT
i
i
n
1
)
1
(
= PMT s
n
i
“s angle n at i”
so our FV = 100
1
01
.
1
1
01
.
1
4
= $406.04
Example
: you need $18,000 in three years to buy a car.
How
much per month should you put into a 6% savings account to
accumulate that amount?
33 Part I
p. 1
end of
month 1
pay
$100
end of
month 2
pay
$100
end of
month 3
pay
$100
end of
month 4
pay
$100
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18000 = PMT
005
.
1
)
005
.
1
(
36
can you solve it?
($457.59)
Creating a schedule (by period)
We can easily compute the future value of a series of
payments using the
future value formula
. Suppose we want
a more detailed report, period by period, that shows:
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 Spring '11
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