# 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) ^{n }- 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