3-3 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
end of
month 1
pay
$100
end of
month 2
pay
$100
end of
month 3
pay
$100
end of
month 4
pay
$100
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:
(1  i ) n  1
FV = PMT
= PMT s
i
n
i
“s angle n at i”
 1.014  1 
 = $406.04
so our FV = 100 

 1.01  1 
3-3 Part I
p. 1
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?
(1.005) 36  1
18000 = PMT
.005
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:
 interest being earned each period
 the value of the investment at the end of each period
This kind of schedule can be created as follows. We will
use our example of 4 monthly payments of $100, earning a
nominal 12% (i = .01)
interest earned
end
PMT during month
month
= i(prev FV)
1
100 0
2
100 1.00
3
100 2.01
4
100 3.03
3-3 Part I
FV (end of month) =
(prev FV) + PMT + interest
100.00
201.00
303.01
406.04
p. 2
Creating a schedule (by year)
Compute FV at end of each year by using the formula
(1  i ) n  1
FV = PMT
i
Compute interest earned during year (e.g., for income tax
purposes) as follows:
FV = (prev FV) + payments + interest
 interest = FV - (prev FV) - payments
end
FV (use formula)
year
100((1.01)12-1)/.01
1
= 1268.25
100((1.01)24-1)/.01
2
= 2697.35
3
4307.69
3-3 Part I
Payments Interest = FV –
(prev FV) - Payments
1200
68.25
1200
229.10
1200
410.34
p. 3