# Present 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. For example, ABC Imports buys a warehouse from Delaney Real Estate for $500,000 and promises to pay for the warehouse with five payments of $100,000, to be paid at intervals of one payment per year; this is an annuity.

You might want to calculate the present value of the annuity, to see how much it is worth today. This is done by using an interest rate to discount the amount of the annuity. The interest rate can be based on the current amount being obtained through other investments, the corporate cost of capital, or some other measure.

An annuity table represents a method for determining the present value of an annuity. The annuity table contains a factor specific to the number of payments over which you expect to receive a series of equal payments and at a certain discount rate. When you multiply this factor by one of the payments, you arrive at the present value of the stream of payments. Thus, if you expect to receive 5 payments of $10,000 each and use a discount rate of 8%, then the factor would be 3.9927 (as noted in the table below in the intersection of the "8%" column and the "n" row of "5". You would then multiply the 3.9927 factor by $10,000 to arrive at a present value of the annuity of $39,927.

**Rate Table For the Present Value of an Ordinary Annuity of 1**

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

1 | 0.9901 | 0.9804 | 0.9709 | 0.9615 | 0.9524 | 0.9434 | 0.9259 | 0.9091 | 0.8929 |

2 | 1.9704 | 1.9416 | 1.9135 | 1.8861 | 1.8594 | 1.8334 | 1.7833 | 1.7355 | 1.6906 |

3 | 2.9410 | 2.8839 | 2.8286 | 2.7751 | 2.7233 | 2.6730 | 2.5771 | 2.4869 | 2.4018 |

4 | 3.9020 | 3.8077 | 3.7171 | 3.6299 | 3.5460 | 3.4651 | 3.3121 | 3.1699 | 3.0374 |

5 | 4.8534 | 4.7135 | 4.5797 | 4.4518 | 4.3295 | 4.2124 | 3.9927 | 3.7908 | 3.6048 |

6 | 5.7955 | 5.6014 | 5.4172 | 5.2421 | 5.0757 | 4.9173 | 4.6229 | 4.3553 | 4.1114 |

7 | 6.7282 | 6.4720 | 6.2303 | 6.0021 | 5.7864 | 5.5824 | 5.2064 | 4.8684 | 4.5638 |

8 | 7.6517 | 7.3255 | 7.0197 | 6.7327 | 6.4632 | 6.2098 | 5.7466 | 5.3349 | 4.9676 |

9 | 8.5660 | 8.1622 | 7.7861 | 7.4353 | 7.1078 | 6.8017 | 6.2469 | 5.7590 | 5.3283 |

10 | 9.4713 | 8.9826 | 8.5302 | 8.1109 | 7.7217 | 7.3601 | 6.7101 | 6.1446 | 5.6502 |

11 | 10.3676 | 9.7869 | 9.2526 | 8.7605 | 8.3064 | 7.8869 | 7.1390 | 6.4951 | 5.9377 |

12 | 11.2551 | 10.5753 | 9.9540 | 9.3851 | 8.8633 | 8.3838 | 7.5361 | 6.8137 | 6.1944 |

13 | 12.1337 | 11.3484 | 10.6350 | 9.9857 | 9.3936 | 8.8527 | 7.9038 | 7.1034 | 6.4236 |

14 | 13.0037 | 12.1063 | 11.2961 | 10.5631 | 9.8986 | 9.2950 | 8.2442 | 7.3667 | 6.6282 |

15 | 13.8651 | 12.8493 | 11.9380 | 11.1184 | 10.3797 | 9.7123 | 8.5595 | 7.6061 | 6.8109 |

16 | 14.7179 | 13.5777 | 12.5611 | 11.6523 | 10.8378 | 10.1059 | 8.8514 | 7.8237 | 6.9740 |

17 | 15.5623 | 14.2919 | 13.1661 | 12.1657 | 11.2741 | 10.4773 | 9.1216 | 8.0216 | 7.1196 |

18 | 16.3983 | 14.9920 | 13.7535 | 12.6593 | 11.6896 | 10.8276 | 9.3719 | 8.2014 | 7.2497 |

19 | 17.2260 | 15.6785 | 14.3238 | 13.1339 | 12.0853 | 11.1581 | 9.6036 | 8.3649 | 7.3658 |

20 | 18.0456 | 16.3514 | 14.8775 | 13.5903 | 12.4622 | 11.4699 | 9.8182 | 8.5136 | 7.4694 |

21 | 18.8570 | 17.0112 | 15.4150 | 14.0292 | 12.8212 | 11.7641 | 10.0168 | 8.6487 | 7.5620 |

22 | 19.6604 | 17.6581 | 15.9369 | 14.4511 | 13.1630 | 12.0416 | 10.2007 | 8.7715 | 7.6447 |

23 | 20.4558 | 18.2922 | 16.4436 | 14.8568 | 13.4886 | 12.3034 | 10.3711 | 8.8832 | 7.7184 |

24 | 21.2434 | 18.9139 | 16.9355 | 15.2470 | 13.7986 | 12.5504 | 10.5288 | 8.9847 | 7.7843 |

25 | 22.0232 | 19.5235 | 17.4132 | 15.6221 | 14.0939 | 12.7834 | 10.6748 | 9.0770 | 7.8431 |

26 | 22.7952 | 20.1210 | 17.8768 | 15.9828 | 14.3752 | 13.0032 | 10.8100 | 9.1610 | 7.8957 |

27 | 23.5596 | 20.7069 | 18.3270 | 16.3296 | 14.6430 | 13.2105 | 10.9352 | 9.2372 | 7.9426 |

28 | 24.3164 | 21.2813 | 18.7641 | 16.6631 | 14.8981 | 13.4062 | 11.0511 | 9.3066 | 7.9844 |

29 | 25.0658 | 21.8444 | 19.1885 | 16.9837 | 15.1411 | 13.5907 | 11.1584 | 9.3696 | 8.0218 |

30 | 25.8077 | 22.3965 | 19.6004 | 17.2920 | 15.3725 | 13.7648 | 11.2578 | 9.4269 | 8.0552 |

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 annuity formula in an electronic spreadsheet to more precisely calculate the correct amount. The formula for calculating the present value of an ordinary annuity is:

**P = PMT [(1 - (1 / (1 + r) ^{n})) / r]**

Where:

P = The present 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

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