Future value of an ordinary annuity table

An annuity is a series of payments that occur at the same intervals and in the same amounts. An example of an annuity is a series of payments from the buyer of an asset to the seller, where the buyer promises to make a series of regular payments. Thus, Harvest Designs buys a warehouse from Higgins Realty for $1,000,000, and promises to pay for the warehouse with five payments of $200,000, to be paid at intervals of one payment per year; this is an annuity. If the payments are due at the end of a period, the annuity is called an ordinary annuity. If the payments are due at the beginning of a period, the annuity is called an annuity due.

You might want to calculate the future value of an annuity, to see how much a series of investments will be worth as of a future date. You do this by using an interest rate to add interest income to the amount of the annuity. The interest rate can be based on the current amount you are obtaining through other investments, the corporate cost of capital, or some other measure.

An annuity table represents a method for determining the future value of an annuity. The annuity table contains a factor specific to the future value of a series of payments, when a certain interest earnings rate is assumed. When you multiply this factor by one of the payments, you arrive at the future value of the stream of payments. For example, if you expect to make 5 payments of $10,000 each into an investment fund and use an interest rate of 6%, then the factor would be 5.6371 (as noted in the table below at the intersection of the "6%" column and the "n" row of "5" periods. You would then multiply the 5.6371 factor by $10,000 to arrive at a future value of the annuity of $56,371.

Rate Table For the Future Value of an Ordinary Annuity of 1

n 1% 2% 3% 4% 5% 6% 8% 10% 12%
1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
2 2.0100 2.0200 2.0300 2.0400 2.0500 2.0600 2.0800 2.1000 2.1200
3 3.0301 3.0604 3.0909 3.1216 3.1525 3.1836 3.2464 3.3100 3.3744
4 4.0604 4.1216 4.1836 4.2465 4.3101 4.3746 4.5061 4.6410 4.7793
5 5.1010 5.2040 5.3091 5.4163 5.5256 5.6371 5.8666 6.1051 6.3529
6 6.1520 6.3081 6.4684 6.6330 6.8019 6.9753 7.3359 7.7156 8.1152
7 7.2135 7.4343 7.6625 7.8983 8.1420 8.3938 8.9228 9.4872 10.0890
8 8.2857 8.5830 8.8923 9.2142 9.5491 9.8975 10.6366 11.4359 12.2997
9 9.3685 9.7546 10.1591 10.5828 11.0266 11.4913 12.4876 13.5795 14.7757
10 10.4622 10.9497 11.4639 12.0061 12.5779 13.1808 14.4866 15.9374 17.5487
11 11.5668 12.1687 12.8078 13.4864 14.2068 14.9716 16.6455 18.5312 20.6546
12 12.6825 13.4121 14.1920 15.0258 15.9171 16.8699 18.9771 21.3843 24.1331
13 13.8093 14.6803 15.6178 16.6268 17.7130 18.8821 21.4953 24.5227 28.0291
14 14.9474 15.9739 17.0863 18.2919 19.5986 21.0151 24.2149 27.9750 32.3926
15 16.0969 17.2934 18.5989 20.0236 21.5786 23.2760 27.1521 31.7725 37.2797
16 17.2579 18.6393 20.1569 21.8245 23.6575 25.6725 30.3243 35.9497 42.7533
17 18.4304 20.0121 21.7616 23.6975 25.8404 28.2129 33.7502 40.5447 48.8837
18 19.6148 21.4123 23.4144 25.6454 28.1324 30.9057 37.4502 45.5992 55.7497
19 20.8109 22.8406 25.1169 27.6712 30.5390 33.7600 41.4463 51.1591 63.4397
20 22.0190 24.2974 26.8704 29.7781 33.0660 36.7856 45.7620 57.2750 72.0524
21 23.2392 25.7833 28.6765 31.9692 35.7193 39.9927 50.4229 64.0025 81.6987
22 24.4716 27.2990 30.5368 34.2480 38.5052 43.3923 55.4568 71.4028 92.5026
23 25.7163 28.8450 32.4529 36.6179 41.4305 46.9958 60.8933 79.5430 104.6029
24 26.9735 30.4219 34.4265 39.0826 44.5020 50.8156 66.7648 88.4973 118.1552
25 28.2432 32.0303 36.4593 41.6459 47.7271 54.8645 73.1059 98.3471 133.3339
26 29.5256 33.6709 38.5530 44.3117 51.1135 59.1564 79.9544 109.1818 150.3339
27 30.8209 35.3443 40.7096 47.0842 54.6691 63.7058 87.3508 121.0999 169.3740
28 32.1291 37.0512 42.9309 49.9676 58.4026 68.5281 95.3388 134.2099 190.6989
29 33.4504 38.7922 45.2189 52.9663 62.3227 73.6398 103.9659 148.6309 214.5828
30 34.7849 40.5681 47.5754 56.0849 66.4389 79.0582 113.2832 164.4940 241.3327

The preceding annuity table is useful as a quick reference, but only provides values for discrete time periods and interest rates that may not exactly correspond to a real-world scenario. Accordingly, use the following annuity formula in an electronic spreadsheet to more precisely calculate the correct amount of the future value of an ordinary annuity:

P = PMT [((1 + r)- 1) / r]

Where:

P = The future value of the annuity stream to be paid in the future

PMT = The amount of each annuity payment

r = The interest rate

n = The number of periods over which payments are made