TIME
VALUE OF MONEY 3-35
Year
Deposit
x
FVIF
=
Payments
1
$100
x
(1.06)
5
=
133.82
2
$000
x
(1.06)
4
=
0.00
3
$350
x
(1.06)
3
=
416.86
4
$250
x
(1.06)
2
=
280.90
5
$200
x
(1.06)
1
=
212.00
6
$000
x
(1.06)
0
=
0.00
FV
=
$1,043.58
Figure 3.6: Future Value of Annuity with Unequal Payments
You can see that the first deposit is in the account for five years,
earning compounded interest of $33.82 during that time; no deposit is
made in the second year; the third deposit earns compound interest for
three years in the amount of $66.86; and so on. The total interest the
account will earn for the six years is $1,043.58 $900.00 (the total
amount of all the deposits) = $143.58.
Formula for
present value
of unequal
payments
The formula for calculating the present value of unequal payments is a
modification of the formula for the present value for an annuity.
PV = CF
1
[1/(1+R)]
1
+ CF
2
[1/(1+R)]
2
+ ... + CF
T
[1/(1+R)]
T
Where:
PV = Present value of the stream of cash flows
CF
i
= Cash flow (payment) in period i
R
= Discount rate
T
= Number of periods in the stream of cash flows
The idea is to discount each payment or cash flow from the time of
receipt back to the present time. The present value is the sum of all of
the discounted cash flows.