# Future value of an annuity due 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, Hobo Clothiers buys a warehouse from Marlowe Realty for $2,000,000, and promises to pay for the warehouse with five payments of $400,000, 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. This can be done 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. Ideally, it should be a rate that you can currently obtain or expect to obtain on the open market.

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 this factor is multiplied by one of the payments, you arrive at the future value of the stream of payments. For example, if there is an expectation to make 8 payments of $10,000 each into an investment fund at the beginning of each period (an annuity due) and use an interest rate of 5%, then the factor would be 10.0266 (as noted in the table below at the intersection of the "5%" column and the "n" row of "8" periods. You would then multiply the 10.0266 factor by $10,000 to arrive at a future value of the annuity of $100,266.

**Rate Table For the Future Value of an Annuity Due of 1**

n | 1% | 2% | 3% | 4% | 5% | 6% | 8% | 10% | 12% |

1 | 1.0100 | 1.0200 | 1.0300 | 1.0400 | 1.0500 | 1.0600 | 1.0800 | 1.1000 | 1.1200 |

2 | 2.0301 | 2.0604 | 2.0909 | 2.1216 | 2.1525 | 2.1836 | 2.2464 | 2.3100 | 2.3744 |

3 | 3.0604 | 3.1216 | 3.1836 | 3.2465 | 3.3101 | 3.3746 | 3.5061 | 3.6410 | 3.7793 |

4 | 4.1010 | 4.2040 | 4.3091 | 4.4163 | 4.5256 | 4.6371 | 4.8666 | 5.1051 | 5.3528 |

5 | 5.1520 | 5.3081 | 5.4684 | 5.6330 | 5.8019 | 5.9753 | 6.3359 | 6.7156 | 7.1152 |

6 | 6.2135 | 6.4343 | 6.6625 | 6.8983 | 7.1420 | 7.3938 | 7.9228 | 8.4872 | 9.0890 |

7 | 7.2857 | 7.5830 | 7.8923 | 8.2142 | 8.5491 | 8.8975 | 9.6366 | 10.4359 | 11.2997 |

8 | 8.3685 | 8.7546 | 9.1591 | 9.5828 | 10.0266 | 10.4913 | 11.4876 | 12.5795 | 13.7757 |

9 | 9.4622 | 9.9497 | 10.4639 | 11.0061 | 11.5779 | 12.1808 | 13.4866 | 14.9374 | 16.5487 |

10 | 10.5668 | 11.1687 | 11.8078 | 12.4864 | 13.2068 | 13.9716 | 15.6455 | 17.5312 | 19.6546 |

11 | 11.6825 | 12.4121 | 13.1920 | 14.0258 | 14.9171 | 15.8699 | 17.9771 | 20.3843 | 23.1331 |

12 | 12.8093 | 13.6803 | 14.6178 | 15.6268 | 16.7130 | 17.8821 | 20.4953 | 23.5227 | 27.0291 |

13 | 13.9474 | 14.9739 | 16.0863 | 17.2919 | 18.5986 | 20.0151 | 23.2149 | 26.9750 | 31.3926 |

14 | 15.0969 | 16.2934 | 17.5989 | 19.0236 | 20.5786 | 22.2760 | 26.1521 | 30.7725 | 36.2797 |

15 | 16.2579 | 17.6393 | 19.1569 | 20.8245 | 22.6575 | 24.6725 | 29.3243 | 34.9497 | 41.7533 |

16 | 17.4304 | 19.0121 | 20.7616 | 22.6975 | 24.8404 | 27.2129 | 32.7502 | 39.5447 | 47.8837 |

17 | 18.6147 | 20.4123 | 22.4144 | 24.6454 | 27.1324 | 29.9057 | 36.4502 | 44.5992 | 54.7497 |

18 | 19.8109 | 21.8406 | 24.1169 | 26.6712 | 29.5390 | 32.7600 | 40.4463 | 50.1591 | 62.4397 |

19 | 21.0190 | 23.2974 | 25.8704 | 28.7781 | 32.0660 | 35.7856 | 44.7620 | 56.2750 | 71.0524 |

20 | 22.2392 | 24.7833 | 27.6765 | 30.9692 | 34.7193 | 38.9927 | 49.4229 | 63.0025 | 80.6987 |

21 | 23.4716 | 26.2990 | 29.5368 | 33.2480 | 37.5052 | 42.3923 | 54.4568 | 70.4027 | 91.5026 |

22 | 24.7163 | 27.8450 | 31.4529 | 35.6179 | 40.4305 | 45.9958 | 59.8933 | 78.5430 | 103.6029 |

23 | 25.9735 | 29.4219 | 33.4265 | 38.0826 | 43.5020 | 49.8156 | 65.7648 | 87.4973 | 117.1552 |

24 | 27.2432 | 31.0303 | 35.4593 | 40.6459 | 46.7271 | 53.8645 | 72.1059 | 97.3471 | 132.3339 |

25 | 28.5256 | 32.6709 | 37.5530 | 43.3117 | 50.1135 | 58.1564 | 78.9544 | 108.1818 | 149.3339 |

26 | 29.8209 | 34.3443 | 39.7096 | 46.0842 | 53.6691 | 62.7058 | 86.3508 | 120.0999 | 168.3740 |

27 | 31.1291 | 36.0512 | 41.9309 | 48.9676 | 57.4026 | 67.5281 | 94.3388 | 133.2099 | 189.6989 |

28 | 32.4504 | 37.7922 | 44.2189 | 51.9663 | 61.3227 | 72.6398 | 102.9659 | 147.6309 | 213.5828 |

29 | 33.7849 | 39.5681 | 46.5754 | 55.0849 | 65.4388 | 78.0582 | 112.2832 | 163.4940 | 240.3327 |

30 | 35.1327 | 41.3794 | 49.0027 | 58.3283 | 69.7608 | 83.8017 | 122.3459 | 180.9434 | 270.2926 |

A glance at the table should make clear the massive impact of interest rate compounding over time. For example, the multiplier associated with a 12% interest rate for thirty periods is more than 270, versus a muliplier of only 84 at a 6% interest rate (which is a difference of 3.2x).

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