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%).