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Future Value of Annuity Due - AccountingTools

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 anordinary annuity . If the payments are due at the beginning of a period, the annuity is called anannuity 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.

Anannuity tablerepresents 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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Category: Annuity