The formula for the future value of an annuity due

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What is Future Value?

Future value is the value of a sum of cash to be paid on a specific date in the future, assuming a certain rate of growth. This value is a critical issue for investors, who want to understand how much money they will have in the future if they take certain investment decisions now.

What is the Formula for the Future Value of an Annuity Due?

An annuity due is a series of payments made at the beginning of each period in the series. Therefore, the formula for the future value of an annuity due refers to the value on a specific future date of a series of periodic payments, where each payment is made at the beginning of a period. Such a stream of payments is a common characteristic of payments made to the beneficiary of a pension plan. These calculations are used by financial institutions to determine the cash flows associated with their products.

How to Calculate the Future Value of an Annuity Due

The formula for calculating the future value of an annuity due (where a series of equal payments are made at the beginning of each of multiple consecutive periods) is:

P = (PMT [((1 + r)n - 1) / r])(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 to be made

This value is the amount that a stream of future payments will grow to, assuming that a certain amount of compounded interest earnings gradually accrue over the measurement period. The calculation is identical to the one used for the future value of an ordinary annuity, except that we add an extra period to account for payments being made at the beginning of each period, rather than the end.

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Example of the Future Value of an Annuity Due

The treasurer of ABC Imports expects to invest $50,000 of the firm's funds in a long-term investment vehicle at the beginning of each year for the next five years. He expects that the company will earn 6% interest that will compound annually. The value that these payments should have at the end of the five-year period is calculated as:

P = ($50,000 [((1 + .06)5 - 1) / .06])(1 + .06)

P = $298,765.90

As another example, what if the interest on the investment compounded monthly instead of annually, and the amount invested were $4,000 at the end of each month? The calculation is:

P = ($4,000 [((1 + .005)60 - 1) / .06])(1 + .005)

P = $280,475.50

The .005 interest rate used in the last example is 1/12th of the full 6% annual interest rate.

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