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© 2014 Pacific Crest
367
M
ethodology
C
alculating the
P
ayout
for a
L
ump
S
um
A
nnuity
Scenario:
You want to put $100,000 into the annuity to start and draw out annual payments
for 20 years. The account earns 7% interest. What will the payout be each year?
Step
Explanation
1. Identify the values
of the variables
Identify the present value
P
(money to be put into the annuity), the number
n
of payouts to be received, the interest rate
r
that the account will earn,
and note that $0 will be left at the end.
WATCH
IT WORK!
P
= 100000
n
= 20
r
= .07 End of period ($0)
2.
Calculate the
payments using a
formula
(1 )
(1 ) 1
n
n
r r
PMT P
r
+
=
+ −
or use the Excel formula PMT:
=
PMT(rate, # of periods, amount, beginning or end of period)
20
20
.07(1.07)
100000
(1.07) 1
PMT
=
−
In Excel, =PMT(.07,20,-100000,0)
This annuity will pay out $9439.29 per year for 20 years.
3.
State the total
amount of the
payouts for the
annuity
Calculate the total amount by multiplying the amount of each payment by
the number of payments and state that amount.
The $100,000 annuity will pay out a total of $188,785.80 over the 20 year period.
4.
Validate
Compare the present value of the payments with the amount initially
invested using the Excel Net Present Value (NPV) function (sum of all
the payment present values). To enter all those equal payments, assign
a name (e.g., pay) to a 20-cell range, such as A1 to A20, where each cell
has the same value: 9439.29.
=
NPV(rate,payments)
=
NPV
(.07,
pay
) = $99,999.97
YOUR
TURN!
Scenario:
$10,000 will be put into the annuity to start, to be paid out in 10 annual
payments. The account earns 8% interest. What will the payout be each year?
8.2 Time Value of Money