Present Value of a Series of $1 Payments

to Be Paid in the Future

This table shows how much a series of $1 payments, to be paid at the end of each    period for a
specified number of periods into the future, is currently worth, with interest at different rates,
compounded annually.    In other words, the table shows what you should be willing to pay,
today, in order to receive a certain series of payments of $1 each.

To use the table, find the vertical column under your interest rate (or cost of capital).    Then find
the horizontal row corresponding to the number of the last year you will receive the payment.   
The point at which the column and the row intersect is your present value of a series of $1
payments.    You can multiply this value by the number of dollars you expect to receive in each
payment, in order to find the present value of the series.

An example showing how to use this table to find the Internal Rate of Return of a major
purchase or project follows the table.

PRESENT WORTH OF ONE DOLLAR PER PERIOD

PAYABLE AT END OF EACH PERIOD

Years 3% 3.5% 4% 4.5%

1 $0.970874 $0.966184 $0.961538 $0.956938
2 $1.913470 $1.899694 $1.886095 $1.872668
3 $2.828611 $2.801637 $2.775091 $2.748964
4 $3.717098 $3.673079 $3.629895 $3.587526
5 $4.579707 $4.515052 $4.451822 $4.389977
6 $5.417191 $5.328553 $5.242137 $5.157872
7 $6.230283 $6.114544 $6.002055 $5.892701
8 $7.019692 $6.873956 $6.732745 $6.595886
9 $7.786109 $7.607687 $7.435332 $7.268790
10 $8.530203 $8.316605 $8.110896 $7.912718
11 $9.252624 $9.001551 $8.760477 $8.528917
12 $9.954004 $9.663334 $9.385074 $9.118581
13 $10.634955 $10.302738 $9.985648 $9.682852
14 $11.296073 $10.920520 $10.563123 $10.222825
15 $11.937935 $11.517411 $11.118387 $10.739546
16 $12.561102 $12.094117 $11.652296 $11.234015
17 $13.166118 $12.651321 $12.165669 $11.707191
18 $13.753513 $13.189682 $12.659297 $12.159992
19 $14.323799 $13.709837 $13.133939 $12.593294
20 $14.877475 $14.212403 $13.590326 $13.007936
21 $15.415024 $14.697974 $14.029160 $13.404724
22 $15.936917 $15.167125 $14.451115 $13.784425
23 $16.443608 $15.620410 $14.856842 $14.147775
24 $16.935542 $16.058368 $15.246963 $14.495478
25 $17.413148 $16.481515 $15.622080 $14.828209

Years 5% 5.5% 6% 6.5%

 1 $0.952381 $0.947867 $0.943396 $0.938967
2 $1.859410 $1.846320 $1.833393 $1.820626
3 $2.723248 $2.697933 $2.673012 $2.648476
4 $3.545951 $3.505150 $3.465106 $3.425799
5 $4.329477 $4.270284 $4.212364 $4.155679
6 $5.075692 $4.995530 $4.917324 $4.841014
7 $5.786373 $5.682967 $5.582381 $5.484520
8 $6.463213 $6.334566 $6.209794 $6.088751
9 $7.107822 $6.952195 $6.801692 $6.656104
10 $7.721735 $7.537626 $7.360087 $7.188830
11 $8.306414 $8.092536 $7.886875 $7.689042
12 $8.863252 $8.618518 $8.383844 $8.158725
13 $9.393573 $9.117079 $8.852683 $8.599742
14 $9.898641 $9.589648 $9.294984 $9.013842
15 $10.379658 $10.037581 $9.712249 $9.402669
16 $10.837770 $10.462162 $10.105895 $9.767764
17 $11.274066 $10.864609 $10.477260 $10.110577
18 $11.689587 $11.246074 $10.827603 $10.432466
19 $12.085321 $11.607654 $11.158116 $10.734710
20 $12.462210 $11.950382 $11.469921 $11.018507
21 $12.821153 $12.275244 $11.764077 $11.284983
22 $13.163003 $12.583170 $12.041582 $11.535196
23 $13.488574 $12.875042 $12.303379 $11.770137
24 $13.798642 $13.151699 $12.550358 $11.990739
25 $14.093945 $13.413933 $12.783356 $12.197877

Years 7% 7.5% 8% 8.5%

1 $0.934579 $0.930233 $0.925926 $0.921659
2 $1.808018 $1.795565 $1.783265 $1.771114
3 $2.624316 $2.600526 $2.577097 $2.554022
4 $3.387211 $3.349326 $3.312127 $3.275597
5 $4.100197 $4.045885 $3.992710 $3.940642
6 $4.766540 $4.693846 $4.622880 $4.553587
7 $5.389289 $5.296601 $5.206370 $5.118514
8 $5.971299 $5.857304 $5.746639 $5.639183
9 $6.515232 $6.378887 $6.246888 $6.119063
10 $7.023582 $6.864081 $6.710081 $6.561348
11 $7.498674 $7.315424 $7.138964 $6.968984
12 $7.942686 $7.735278 $7.536078 $7.344686
13 $8.357651 $8.125840 $7.903776 $7.690955
14 $8.745468 $8.489154 $8.244237 $8.010097
15 $9.107914 $8.827120 $8.559479 $8.304237
16 $9.446649 $9.141507 $8.851369 $8.575333
17 $9.763223 $9.433960 $9.121638 $8.825192
18 $10.059087 $9.706009 $9.371887 $9.055476
19 $10.335595 $9.959078 $9.603599 $9.267720
20 $10.594014 $10.194491 $9.818147 $9.463337
21 $10.835527 $10.413480 $10.016803 $9.643628
22 $11.061240 $10.617191 $10.200744 $9.809796
 23 $11.272187 $10.806689 $10.371059 $9.962945
24 $11.469334 $10.982967 $10.528758 $10.104097
25 $11.653583 $11.146946 $10.674776 $10.234191

Years 9% 9.5% 10% 10.5%

1 $0.917431 $0.913242 $0.909091 $0.904977
2 $1.759111 $1.747253 $1.735537 $1.723961
3 $2.531295 $2.508907 $2.486852 $2.465123
4 $3.239720 $3.204481 $3.169865 $3.135858
5 $3.889651 $3.839709 $3.790787 $3.742858
6 $4.485919 $4.419825 $4.355261 $4.292179
7 $5.032953 $4.949612 $4.868419 $4.789303
8 $5.534819 $5.433436 $5.334926 $5.239188
9 $5.995247 $5.875284 $5.759024 $5.646324
10 $6.417658 $6.278798 $6.144567 $6.014773
11 $6.805191 $6.647304 $6.495061 $6.348211
12 $7.160725 $6.983839 $6.813692 $6.649964
13 $7.486904 $7.291178 $7.103356 $6.923045
14 $7.786150 $7.571852 $7.366687 $7.170176
15 $8.060688 $7.828175 $7.606080 $7.393825
16 $8.312558 $8.062260 $7.823709 $7.596221
17 $8.543631 $8.276037 $8.021553 $7.779386
18 $8.755625 $8.471266 $8.201412 $7.945146
19 $8.950115 $8.649558 $8.364920 $8.095154
20 $9.128546 $8.812382 $8.513564 $8.230909
21 $9.292244 $8.961080 $8.648694 $8.353764
22 $9.442425 $9.096876 $8.771540 $8.464945
23 $9.580207 $9.220892 $8.883218 $8.565561
24 $9.706612 $9.334148 $8.984744 $8.656616
25 $9.822580 $9.437578 $9.077040 $8.739019

Years 11% 11.5% 12% 12.5%

1 $0.900901 $0.896861 $0.892857 $0.888889
2 $1.712523 $1.701221 $1.690051 $1.679012
3 $2.443715 $2.422619 $2.401831 $2.381344
4 $3.102446 $3.069614 $3.037349 $3.005639
5 $3.695897 $3.649878 $3.604776 $3.560568
6 $4.230538 $4.170294 $4.111407 $4.053839
7 $4.712196 $4.637035 $4.563757 $4.492301
8 $5.146123 $5.055637 $4.967640 $4.882045
9 $5.537048 $5.431064 $5.328250 $5.228485
10 $5.889232 $5.767771 $5.650223 $5.536431
11 $6.206515 $6.069750 $5.937699 $5.810161
12 $6.492356 $6.340583 $6.194374 $6.053476
13 $6.749870 $6.583482 $6.423548 $6.269757
14 $6.981865 $6.801329 $6.628168 $6.462006
15 $7.190870 $6.996708 $6.810864 $6.632894
16 $7.379162 $7.171935 $6.973986 $6.784795
 17 $7.548794 $7.329090 $7.119630 $6.919818
18 $7.701617 $7.470036 $7.249670 $7.039838
19 $7.839294 $7.596445 $7.365777 $7.146523
20 $7.963328 $7.709816 $7.469444 $7.241353
21 $8.075070 $7.811494 $7.562003 $7.325647
22 $8.175739 $7.902685 $7.644646 $7.400575
23 $8.266432 $7.984471 $7.718434 $7.467178
24 $8.348137 $8.057822 $7.784316 $7.526381
25 $8.421745 $8.123607 $7.843139 $7.579005

Years 13% 13.5% 14% 14.5%

1 $0.884956 $0.881057 $0.877193 $0.873362
2 $1.668102 $1.657319 $1.646661 $1.636124
3 $2.361153 $2.341250 $2.321632 $2.302292
4 $2.974471 $2.943833 $2.913712 $2.884098
5 $3.517231 $3.474743 $3.433081 $3.392225
6 $3.997550 $3.942505 $3.888668 $3.836005
7 $4.422610 $4.354630 $4.288305 $4.223585
8 $4.798770 $4.717735 $4.638864 $4.562083
9 $5.131655 $5.037652 $4.946372 $4.857714
10 $5.426243 $5.319517 $5.216116 $5.115908
11 $5.686941 $5.567857 $5.452733 $5.341404
12 $5.917647 $5.786658 $5.660292 $5.538344
13 $6.121812 $5.979434 $5.842362 $5.710344
14 $6.302488 $6.149281 $6.002072 $5.860563
15 $6.462379 $6.298926 $6.142168 $5.991758
16 $6.603875 $6.430772 $6.265060 $6.106339
17 $6.729093 $6.546936 $6.372859 $6.206409
18 $6.839905 $6.649283 $6.467420 $6.293807
19 $6.937969 $6.739456 $6.550369 $6.370137
20 $7.024752 $6.818904 $6.623131 $6.436801
21 $7.101550 $6.888902 $6.686957 $6.495023
22 $7.169513 $6.950575 $6.742944 $6.545871
23 $7.229658 $7.004912 $6.792056 $6.590281
24 $7.282883 $7.052786 $6.835137 $6.629066
25 $7.329985 $7.094965 $6.872927 $6.662940

Years 15%
1 $0.869565
2 $1.625709
3 $2.283225
4 $2.854978
5 $3.352155
6 $3.784483
7 $4.160420
8 $4.487322
9 $4.771584
10 $5.018769
11 $5.233712
 12 $5.420619
13 $5.583147
14 $5.724476
15 $5.847370
16 $5.954235
17 $6.047161
18 $6.127966
19 $6.198231
20 $6.259331
21 $6.312462
22 $6.358663
23 $6.398837
24 $6.433771
25 $6.464149

Example:    As an example of how the table can be used to compute the Internal Rate of Return
of a major project, consider the following:

Sellars, Inc. is considering the purchase of a new computer system that will cost $7,500, but will
allow it to save about $2,000 a year in desktop publishing expenses.

If you want to use the annuity tables to calculate the IRR of Sellars’ project, you must first
compute the number to look up in the tables.    You can do this by dividing the expected net cash
outflow (costs) for the project by the expected average annual net cash inflow (savings).    In this
case, the cost of the project (net cash outflow) is $7,500, and the average annual net cash
inflow is $2,000.

$7,500 ÷ $2,000 = 3.75

Then, look at the row corresponding to the number of years the project or equipment will be in
use (in this case, five).    Look across the rows until you find the number that is closest to the
result you found (3.75).    Then look at the top of the column in which the closest number was
found, to see the interest rate that is Sellars’ IRR (in this case, 10%).