An Annuity is a bunch of structured payments or equal payments made regularly, like every month or every week.
You win the lottery. The lottery guy comes to your
house and says you have to choose between getting $
1,000,000 now in one lump sum, or getting structured payments of $ 50,000 a year
for the next 22 years. Which do you take?? Or, similarly, let's say you were
injured on the job or whatever and were awarded an annuity of structured payments
of $50,000 a year for the next 22 years. Perhaps you want to sell your annuity
(the payments) to someone and get a lump sum of cash today. Is it worth $1,000,000?
First you have to choose an interest rate. Money is
generally worth less in the future, right? So that
$50,000 payment you get in 22 years is not going to be
worth as much as it is today? You know, stuff will be
more expensive then, right? So guess an interest rate, in
this case, the rate of inflation for the next 22 years.
Lets say 4%. Now, you have to figure out what is the
present value of the $50,000 times 22 years discounted by
4% and then compare it with the million bucks. There are
basically 2 ways to do this.
Use a financial calculator.
Use an annuity table.
Use a financial calculator - The PV of an
Annuity.
Enter n (the number of compounding periods - in
this case the number of years). Press 22 and then
push the N button.
Enter i (the interest rate per period - in this
case the number of years). Press 4 and then push
the i button.
Enter FV (the future value). It is zero. You want
to know the Present Value, not the future value,
right? Push 0 and then push the FV button.
Enter PMT (the payment). You are not making a
payment, you are getting one. So you have to show
a negative number. Press 50000, then the CHS
(change sign button), then push the PMT button.
Push the PV (present value) button.
Answer = $722,555. This means 22 annual structured payments
of 50,000 each is worth only $722,555 of today's
dollars. So you should take the million bucks
from the lottery guy in one lump sum.
Use an annuity table - The PV of an Annuity.
Somewhere in your book, I bet there is a table that
looks something like this:
1%
2%
3%
4%
1
00.9901
00.9804
00.9703
00.9615
2
01.9704
01.9416
01.9135
01.8861
3
02.9410
02.8839
02.8286
02.7751
4
03.9020
03.8077
03.7171
03.6299
5
04.8534
04.7135
04.5797
04.4518
6
05.7955
05.6014
05.4172
05.2421
7
06.7282
06.4720
06.2302
06.0021
8
07.6517
07.3255
07.0197
06.7327
9
08.5660
08.1622
07.7861
07.4353
10
09.4713
08.9826
08.5302
08.1109
11
10.3676
09.7868
09.2526
08.7605
12
11.2551
10.5753
09.9450
09.3851
13
12.1337
11.3484
10.6350
09.9856
14
13.0037
12.1062
11.2961
10.5631
15
13.8651
12.8493
11.9379
11.1184
16
14.7179
13.5777
12.5611
11.6523
17
15.5623
14.2919
13.1661
12.1657
18
16.3983
14.9920
13.7535
12.6593
19
17.2260
15.6785
14.3238
13.1339
20
18.0456
16.3541
14.8775
13.5903
21
18.8570
17.0112
15.4150
14.0292
22
19.6604
17.6580
15.9369
14.4511
Find this table.
On the left, find the number of compounding
periods (in this case years) - 22
On the top, find the interest rate - 4%
Find below where they meet. It says 14.4511
Multiply 14.4511 times the Payment - $50,000
Answer = $722,555. This means 22 annual structured payments
of 50,000 each is worth only $722,555 of today's
dollars. So you should take the million bucks
from the lottery guy in one lump sum.
Author: Mark McCracken is a corporate trainer and author living in Higashi Osaka, Japan. He is the author of thousands of online articles as well as the Business English textbook, "25 Business Skills in English".