Present Value of $1 to Be Paid in the Future

This table shows how much $1, to be paid at the end of various periods in the future, is currently worth, with interest at different rates, compounded annually.

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 years it will take to receive the payment. The point at which the column and the row intersect is your present value of $1. You can multiply this value by the number of dollars you expect to receive, in order to find the present value of the amount you expect.

An example showing how to use this table to find the Net Present Value of a major purchase or project follows the table.

Present Value of $1 to be Paid in Future

Years 3.0% 3.5% 4.0% 4.5%
1 $0.970874 $0.966184 $0.961538 $0.956938
2 $0.942596 $0.933511 $0.924556 $0.915730
3 $0.915142 $0.901943 $0.888996 $0.876297
4 $0.888487 $0.871442 $0.854804 $0.838561
5 $0.862609 $0.841973 $0.821927 $0.802451
6 $0.837484 $0.813501 $0.790315 $0.767896
7 $0.813092 $0.785991 $0.759918 $0.734828
8 $0.789409 $0.759412 $0.730690 $0.703185
9 $0.766417 $0.733731 $0.702587 $0.672904
10 $0.744094 $0.708919 $0.675564 $0.643928
11 $0.722421 $0.684946 $0.649581 $0.616199
12 $0.701380 $0.661783 $0.624597 $0.589664
13 $0.680951 $0.639404 $0.600574 $0.564272
14 $0.661118 $0.617782 $0.577475 $0.539973
15 $0.641862 $0.596891 $0.555265 $0.516720
16 $0.623167 $0.576706 $0.533908 $0.494469
17 $0.605016 $0.557204 $0.513373 $0.473176
18 $0.587395 $0.538361 $0.493628 $0.452800
19 $0.570286 $0.520156 $0.474642 $0.433302
20 $0.553676 $0.502566 $0.456387 $0.414643
21 $0.537549 $0.485571 $0.438834 $0.396787
22 $0.521893 $0.469151 $0.421955 $0.379701
23 $0.506692 $0.453286 $0.405726 $0.363350
24 $0.491934 $0.437957 $0.390121 $0.347703
25 $0.477606 $0.423147 $0.375117 $0.332731
Years 5.0% 5.5% 6.0% 6.5%
1 $0.952381 $0.947867 $0.943396 $0.938967
2 $0.907029 $0.898452 $0.889996 $0.881659
3 $0.863838 $0.851614 $0.839619 $0.827849
4 $0.822702 $0.807217 $0.792094 $0.777323
5 $0.783526 $0.765134 $0.747258 $0.729881
6 $0.746215 $0.725246 $0.704961 $0.685334
7 $0.710681 $0.687437 $0.665057 $0.643506
8 $0.676839 $0.651599 $0.627412 $0.604231
9 $0.644609 $0.617629 $0.591898 $0.567353
10 $0.613913 $0.585431 $0.558395 $0.532726
11 $0.584679 $0.554911 $0.526788 $0.500212
12 $0.556837 $0.525982 $0.496969 $0.469683
13 $0.530321 $0.498561 $0.468839 $0.441017
14 $0.505068 $0.472569 $0.442301 $0.414100
15 $0.481017 $0.447933 $0.417265 $0.388827
16 $0.458112 $0.424581 $0.393646 $0.365095
17 $0.436297 $0.402447 $0.371364 $0.342813
18 $0.415521 $0.381466 $0.350344 $0.321890
19 $0.395734 $0.361579 $0.330513 $0.302244
20 $0.376889 $0.342729 $0.311805 $0.283797
21 $0.358942 $0.324862 $0.294155 $0.266476
22 $0.341850 $0.307926 $0.277505 $0.250212
23 $0.325571 $0.291873 $0.261797 $0.234941
24 $0.310068 $0.276657 $0.246979 $0.220602
25 $0.295303 $0.262234 $0.232999 $0.207138
Years 7.0% 7.5% 8.0% 8.5%
1 $0.934579 $0.930233 $0.925926 $0.921659
2 $0.873439 $0.865333 $0.857339 $0.849455
3 $0.816298 $0.804961 $0.793832 $0.782908
4 $0.762895 $0.748801 $0.735030 $0.721574
5 $0.712986 $0.696559 $0.680583 $0.665045
6 $0.666342 $0.647962 $0.630170 $0.612945
7 $0.622750 $0.602755 $0.583490 $0.564926
8 $0.582009 $0.560702 $0.540269 $0.520669
9 $0.543934 $0.521583 $0.500249 $0.479880
10 $0.508349 $0.485194 $0.463193 $0.442285
11 $0.475093 $0.451343 $0.428883 $0.407636
12 $0.444012 $0.419854 $0.397114 $0.375702
13 $0.414964 $0.390562 $0.367698 $0.346269
14 $0.387817 $0.363313 $0.340461 $0.319142
15 $0.362446 $0.337966 $0.315242 $0.294140
16 $0.338735 $0.314387 $0.291890 $0.271097
17 $0.316574 $0.292453 $0.270269 $0.249859
18 $0.295864 $0.272049 $0.250249 $0.230285
19 $0.276508 $0.253069 $0.231712 $0.212244
20 $0.258419 $0.235413 $0.214548 $0.195616
21 $0.241513 $0.218989 $0.198656 $0.180292
22 $0.225713 $0.203711 $0.183941 $0.166167
23 $0.210947 $0.189498 $0.170315 $0.153150
24 $0.197147 $0.176277 $0.157699 $0.141152
25 $0.184249 $0.163979 $0.146018 $0.130094
Years 9.0% 9.5% 10.0% 10.5%
1 $0.917431 $0.913242 $0.909091 $0.904977
2 $0.841680 $0.834011 $0.826446 $0.818984
3 $0.772183 $0.761654 $0.751315 $0.741162
4 $0.708425 $0.695574 $0.683013 $0.670735
5 $0.649931 $0.635228 $0.620921 $0.607000
6 $0.596267 $0.580117 $0.564474 $0.549321
7 $0.547034 $0.529787 $0.513158 $0.497123
8 $0.501866 $0.483824 $0.466507 $0.449885
9 $0.460428 $0.441848 $0.424098 $0.407136
10 $0.422411 $0.403514 $0.385543 $0.368449
11 $0.387533 $0.368506 $0.350494 $0.333438
12 $0.355535 $0.336535 $0.318631 $0.301754
13 $0.326179 $0.307338 $0.289664 $0.273080
14 $0.299246 $0.280674 $0.263331 $0.247132
15 $0.274538 $0.256323 $0.239392 $0.223648
16 $0.251870 $0.234085 $0.217629 $0.202397
17 $0.231073 $0.213777 $0.197845 $0.183164
18 $0.211994 $0.195230 $0.179859 $0.165760
19 $0.194490 $0.178292 $0.163508 $0.150009
20 $0.178431 $0.162824 $0.148644 $0.135755
21 $0.163698 $0.148697 $0.135131 $0.122855
22 $0.150182 $0.135797 $0.122846 $0.111181
23 $0.137781 $0.124015 $0.111678 $0.100616
24 $0.126405 $0.113256 $0.101526 $0.091055
25 $0.115968 $0.103430 $0.092296 $0.082403
Years 11.0% 11.5% 12.0% 12.5%
1 $0.900901 $0.896861 $0.892857 $0.888889
2 $0.811622 $0.804360 $0.797194 $0.790123
3 $0.731191 $0.721399 $0.711780 $0.702332
4 $0.658731 $0.646994 $0.635518 $0.624295
5 $0.593451 $0.580264 $0.567427 $0.554929
6 $0.534641 $0.520416 $0.506631 $0.493270
7 $0.481658 $0.466741 $0.452349 $0.438462
8 $0.433926 $0.418602 $0.403883 $0.389744
9 $0.390925 $0.375428 $0.360610 $0.346439
10 $0.352184 $0.336706 $0.321973 $0.307946
11 $0.317283 $0.301979 $0.287476 $0.273730
12 $0.285841 $0.270833 $0.256675 $0.243315
13 $0.257514 $0.242900 $0.229174 $0.216280
14 $0.231995 $0.217847 $0.204620 $0.192249
15 $0.209004 $0.195379 $0.182696 $0.170888
16 $0.188292 $0.175227 $0.163122 $0.151901
17 $0.169633 $0.157155 $0.145644 $0.135023
18 $0.152822 $0.140946 $0.130040 $0.120020
19 $0.137678 $0.126409 $0.116107 $0.106685
20 $0.124034 $0.113371 $0.103667 $0.094831
21 $0.111742 $0.101678 $0.092560 $0.084294
22 $0.100669 $0.091191 $0.082643 $0.074928
23 $0.090693 $0.081786 $0.073788 $0.066603
24 $0.081705 $0.073351 $0.065882 $0.059202
25 $0.073608 $0.065785 $0.058823 $0.052624
Years 13.0% 13.5% 14.0% 14.5%
1 $0.884956 $0.881057 $0.877193 $0.873362
2 $0.783147 $0.776262 $0.769468 $0.762762
3 $0.693050 $0.683931 $0.674972 $0.666168
4 $0.613319 $0.602583 $0.592080 $0.581806
5 $0.542760 $0.530910 $0.519369 $0.508127
6 $0.480319 $0.467762 $0.455587 $0.443779
7 $0.425061 $0.412125 $0.399637 $0.387580
8 $0.376160 $0.363106 $0.350559 $0.338498
9 $0.332885 $0.319917 $0.307508 $0.295631
10 $0.294588 $0.281865 $0.269744 $0.258193
11 $0.260698 $0.248339 $0.236617 $0.225496
12 $0.230706 $0.218801 $0.207559 $0.196940
13 $0.204165 $0.192776 $0.182069 $0.172000
14 $0.180677 $0.169847 $0.159710 $0.150218
15 $0.159891 $0.149645 $0.140096 $0.131195
16 $0.141496 $0.131846 $0.122892 $0.114581
17 $0.125218 $0.116164 $0.107800 $0.100071
18 $0.110812 $0.102347 $0.094561 $0.087398
19 $0.098064 $0.090173 $0.082948 $0.076330
20 $0.086782 $0.079448 $0.072762 $0.066664
21 $0.076798 $0.069998 $0.063826 $0.058222
22 $0.067963 $0.061672 $0.055988 $0.050849
23 $0.060144 $0.054337 $0.049112 $0.044409
24 $0.053225 $0.047874 $0.043081 $0.038785
25 $0.047102 $0.042180 $0.037790 $0.033874
Years 15.0%      
1 $0.869565
2 $0.756144
3 $0.657516
4 $0.571753
5 $0.497177
6 $0.432328
7 $0.375937
8 $0.326902
9 $0.284262
10 $0.247185
11 $0.214943
12 $0.186907
13 $0.162528
14 $0.141329
15 $0.122894
16 $0.106865
17 $0.092926
18 $0.080805
19 $0.070265
20 $0.061100
21 $0.053131
22 $0.046201
23 $0.040174
24 $0.034934
25 $0.030378

Example: As an example of how the table can be used to compute the net present value of a major project, consider the following:

Traders, Inc. is considering the acquisition of a new machine. After all the factors are considered (including initial costs, tax savings from depreciation, revenue from additional sales, and taxes on additional revenues), Traders projects the following cash flows from the machine:

Year 1: ($10,000)

Year 2: $ 3,000

Year 3: $ 3,500

Year 4: $ 3,500

Year 5: $ 3,000

Assume that Traders’ cost of capital is 9%, using the net present value table shows whether the new machine would at least cover its financial costs:

Year Cash Flow Table Factor Present Value
1 ($10,000) x 1.000000 = ($10,000.00)
2 $ 3,000 x 0.917431 = $2,752.29
3 $ 3,500 x 0.841680 = $2,945.88
4 $ 3,500 x 0.772183 = $2,702.64
5 $ 3,000 x 0.708425 = $2,125.28
      —————-
    NPV = $ 526.09

Since the net present value of the cash flow is positive, the purchase of the new machine would be at least slightly profitable for Traders.


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%).

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