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# Present Value of Ordinary Annuity

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, 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 by using an interest rate to discount 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 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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Category: Annuity