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Present Value of An Annuity:
(1-(1 + i)-n)/i

The present value of an annuity in which the yearly payment at the end of each of n years is A, at an interest rate i compounded annually, is P = A(1-(1 + i)-n)/i.

How To Use:

  • You need to find the present value for an annuity in which $1000 is invested at the end of each year for the next 5 years at a discount rate of 7% p.a.
  • Find the column with N Years = 5
  • Find the row 7½%, the number inside the cell is 4.04588
  • The present value for the annuity would be 1000 × 4.04588 = $4045.88
i %N Years
12345678910
10.990101.970402.940993.901974.853435.795486.728197.651688.566029.47130
0.987651.963122.926533.878064.817845.746016.662737.568128.462349.34553
0.985221.955882.912203.854384.782645.697196.598217.485938.360529.22218
0.982801.948702.897983.830944.747865.649006.534647.405058.260499.10122
20.980391.941562.883883.807734.713465.601436.471997.325488.162248.98259
0.978001.934472.869903.784744.679455.554486.410257.247188.065718.86622
0.975611.927422.856023.761974.645835.508136.349397.170147.970878.75206
0.973241.920422.842263.739434.612585.462376.289417.094317.877688.64008
30.970871.913472.828613.717104.579715.417196.230287.019697.786118.53020
0.968521.906562.815073.694984.547205.372596.172006.946257.696128.42240
0.966181.899692.801643.673084.515055.328556.114546.873967.607698.31661
0.963861.892872.788313.651384.483265.285076.057906.802807.520778.21279
12345678910
40.961541.886092.775093.629904.451825.242146.002056.732747.435338.11090
0.959231.879362.761983.608614.420735.199745.946996.663787.351358.01089
0.956941.872672.748963.587534.389985.157875.892706.595897.268797.91272
0.954651.866022.736063.566644.359565.116535.839176.529047.187627.81635
50.952381.859412.723253.545954.329485.075695.786376.463217.107827.72173
0.950121.852842.710543.525454.299725.035365.734316.398407.029357.62884
0.947871.846322.697933.505154.270284.995535.682976.334576.952207.53763
0.945631.839842.685423.485034.241174.956195.632336.271706.876327.44805
60.943401.833392.673013.465114.212364.917325.582386.209796.801697.36009
0.941181.826992.660703.445364.183874.878945.533126.148826.728307.27369
0.938971.820632.648483.425804.155684.841015.484526.088756.656107.18883
0.936771.814302.636353.406424.127794.803555.436586.029586.585097.10547
12345678910
70.934581.808022.624323.387214.100204.766545.389295.971306.515237.02358
0.932401.801772.612383.368184.072904.729975.342635.913886.446516.94313
0.930231.795572.600533.349334.045884.693855.296605.857306.378896.86408
0.928071.789402.588773.330644.019164.658155.251185.801566.312366.78641
80.925931.783262.577103.312133.992714.622885.206375.746646.246896.71008
0.923791.777172.565523.293783.966544.588035.162155.692526.182466.63507
0.921661.771112.554023.275603.940644.553595.118515.639186.119066.56135
0.919541.765092.542623.257583.915014.519555.075455.586626.056666.48889
90.917431.759112.531293.239723.889654.485925.032955.534825.995256.41766
0.915331.753162.520063.222023.864554.452684.991015.483765.934796.34764
0.913241.747252.508913.204483.839714.419834.949615.433445.875286.27880
0.911161.741382.497843.187103.815124.387354.908755.383835.816706.21112
100.909091.735542.486853.169873.790794.355264.868425.334935.759026.14457


i %N Years
11121314151617181920
110.367611.255112.133713.003713.865114.717915.562316.398317.226018.0456
10.217811.079311.930212.770613.600514.420315.229916.029516.819317.5993
10.071110.907511.731512.543413.343214.131314.907615.672616.426217.1686
9.9274910.739511.537612.322013.092913.850514.595115.326916.046116.7529
29.7868510.575311.348412.106212.849313.577714.291914.992015.678516.3514
9.6491110.414811.163611.895912.612213.312613.997714.667715.322915.9637
9.5142110.257810.983211.690912.381413.055013.712214.353414.978915.5892
9.3820710.104210.807011.491012.156712.804613.435114.048814.646015.2273
39.252629.9540010.635011.296111.937912.561113.166113.753514.323814.8775
9.125819.8070810.466911.106011.724912.324412.904913.467314.011914.5393
9.001559.6633310.302710.920511.517412.094112.651313.189713.709814.2124
8.879799.5226910.142410.739611.315311.870212.405012.920513.417313.8962
11121314151617181920
48.760489.385079.9856510.563111.118411.652312.165712.659313.133913.5903
8.643549.250399.8325110.390910.926511.440311.933212.405912.859413.2944
8.528929.118589.6828510.222810.739511.234011.707212.160012.593313.0079
8.416568.989569.5365710.058810.557311.033211.487611.921312.335412.7307
58.306418.863259.393579.8986410.379710.837811.274111.689612.085312.4622
8.198428.739599.253779.7423010.206510.647511.066511.464611.842812.2022
8.092548.618529.117089.5896510.037610.462210.864611.246111.607711.9504
7.988708.499968.983419.440589.8728910.281710.668311.033811.379511.7064
67.886878.383848.852689.294989.7122510.105910.477310.827611.158111.4699
7.787008.270128.724829.152779.555559.9346310.291410.627210.943311.2407
7.689048.158738.599749.013849.402679.7677610.110610.432510.734711.0185
7.592958.049608.477388.878109.253499.605159.9345610.243210.532210.8030
11121314151617181920
77.498677.942698.357658.745479.107919.446659.7632210.059110.335610.5940
7.406187.837938.240498.615858.965829.292149.596409.8801010.144610.3912
7.315427.735288.125848.489158.827129.141519.433969.706019.9590810.1945
7.226377.634688.013628.365318.691708.994629.275759.536669.7788010.0035
87.138967.536087.903788.244248.559488.851379.121649.371899.603609.81815
7.053187.439437.796248.125868.430358.711648.971499.211549.433309.63815
6.968987.344697.690958.010108.304248.575338.825199.055489.267729.46334
6.886337.251807.587867.896888.181048.442348.682618.903559.106719.29353
96.805197.160737.486907.786158.060698.312568.543638.755638.950119.12855
6.725537.071427.388037.677837.943098.185908.408148.611578.797788.96822
6.647306.983847.291187.571857.828188.062268.276048.471278.649568.81238
6.570496.897947.196307.468167.715867.941568.147218.334598.505328.66088
106.495066.813697.103367.366697.606087.823718.021558.201418.364928.51356


i %N Years
21222324252627282930
118.857019.660420.455821.243422.023222.795223.559624.316425.065825.8077
18.369719.130619.882020.624221.357322.081322.796323.502524.200024.8889
17.900118.620819.330920.030420.719621.398622.067622.726723.376124.0158
17.447518.130318.801219.460720.108820.745721.371721.987022.591623.1858
217.011217.658018.292218.913919.523520.121020.706921.281321.844422.3965
16.590417.203417.802818.389018.962419.523120.071520.607821.132321.6453
16.184516.765417.332117.885018.424418.950619.464019.964920.453520.9303
15.792916.343516.879317.400817.908318.402318.883019.350819.806220.2493
315.415015.936916.443616.935517.413117.876818.327018.764119.188519.6004
15.050215.545016.024216.488316.937917.373217.794918.203318.598818.9819
14.698015.167115.620416.058416.481516.890417.285417.667018.035818.3920
14.357814.802715.231515.644816.043216.427216.797317.154017.497817.8292
21222324252627282930
414.029214.451114.856815.247015.622115.982816.329616.663116.983717.2920
13.711614.111914.495814.864115.217315.556215.881216.193016.492116.7790
13.404713.784414.147814.495514.828215.146615.451315.742916.021916.2889
13.108013.468313.812214.140514.454014.753215.038915.311615.571915.8204
512.821213.163013.488613.798614.093914.375214.643014.898115.141115.3725
12.543712.868113.176313.469213.747514.011814.263014.501714.728514.9439
12.275212.583212.875013.151713.413913.662513.898114.121414.333114.5337
12.015512.307812.584212.845613.092713.326513.547513.756513.954114.1410
611.764112.041612.303412.550412.783413.003213.210513.406213.590713.7648
11.520711.784212.032212.265612.485212.692012.886613.069713.242113.4043
11.285011.535211.770111.990712.197912.392412.575012.746512.907513.0587
11.056711.294311.516911.725511.920812.103812.275212.435812.586212.7272
21222324252627282930
710.835511.061211.272211.469311.653611.825811.986712.137112.277712.4090
10.621210.835611.035511.222011.395811.557811.708911.849811.981212.1037
10.413510.617210.806710.983011.146911.299511.441411.573411.696211.8104
10.212110.405710.585310.752010.906711.050311.183611.307311.422111.5286
810.016810.200710.371110.528810.674810.810010.935211.051111.158411.2578
9.8273910.002210.163710.312910.450710.578010.695610.804310.904610.9974
9.643639.809809.9629510.104110.234210.354110.464610.566510.660310.7468
9.465319.623289.768539.9021010.024910.137910.241710.337210.425010.5058
99.292249.442439.580219.706619.822589.9289710.026610.116110.198310.2737
9.124239.267039.397749.517389.626899.727139.818889.902879.9797410.0501
8.961089.096889.220899.334159.437589.532039.618309.697079.769029.83472
8.802628.931789.049459.156689.254389.343409.424519.498419.565759.62711
108.648698.771548.883228.984749.077049.160959.237229.306579.369619.42691


i %N Years
31323334353637383940
126.542327.269627.989728.702729.408630.107530.799531.484732.163032.8347
25.569326.241326.905027.560528.207928.847329.478830.102530.718531.3269
24.646125.267125.879026.481727.075627.660728.237128.805129.364629.9158
23.769924.343924.908025.462426.007326.542827.069027.586328.094628.5942
222.937723.468323.988624.498624.998625.488825.969526.440626.902627.3555
22.147022.637723.117523.586824.045824.494724.933725.363025.782926.1935
21.395421.849222.291922.723823.145223.556323.957324.348624.730325.1028
20.680621.100321.508821.906422.293322.669923.036423.393123.740224.0781
320.000420.388820.765821.131821.487221.832322.167222.492522.808223.1148
19.352919.712320.060320.397420.723921.040121.346321.642921.930222.2084
18.736319.068919.390219.700720.000720.290520.570520.841121.102521.3551
18.148718.456518.753319.039319.315019.580719.836920.083720.321720.5510
31323334353637383940
417.588517.873618.147618.411218.664618.908319.142619.367919.584519.7928
17.054217.318217.571417.814318.047318.270818.485218.690818.888119.0773
16.544416.788917.022917.246817.461017.666017.862218.050018.229718.4016
16.057716.284216.500416.706816.903917.092017.271617.443117.606817.7630
515.592815.802716.002516.192916.374216.546916.711316.867917.017017.1591
15.148615.343115.527915.703415.870316.028716.179316.322416.458316.5875
14.723914.904215.075115.237015.390615.536115.674015.804715.928716.0461
14.317814.484914.642914.792314.933715.067315.193715.313115.426115.5330
613.929114.084014.230214.368114.498214.621014.736814.846014.949115.0463
13.557013.700713.836013.963314.083114.195814.302014.401814.495814.5843
13.200613.333913.459113.576613.687013.790613.887913.979214.065014.1455
12.859212.982813.098713.207213.308813.404113.493313.576813.655113.7284
31323334353637383940
712.531812.646612.753812.854012.947713.035213.117013.193513.264913.3317
12.217912.324412.423612.516212.602512.683012.758112.828012.893312.9541
11.916612.015512.107412.192912.272512.346512.415412.479412.539012.5944
11.627511.719211.804411.883411.956812.024912.088012.146712.201112.2516
811.349811.435011.513911.586911.654611.717211.775211.828911.878611.9246
11.083011.162111.235211.302811.365111.422811.476011.525211.570611.6125
10.826610.900110.967811.030211.087811.140811.189711.234711.276311.3145
10.580010.648310.711110.768810.821910.870710.915610.956910.994811.0297
910.342810.406210.464410.517810.566810.611810.653010.690810.725510.7574
10.114510.173510.227410.276810.322010.363410.401310.436010.467710.4968
9.894729.949529.9995610.045310.087010.125110.159910.191710.220710.2472
9.683019.733959.780379.822669.861199.896309.928299.957449.9840010.0082
109.479019.526389.569439.608579.644169.676519.705929.732659.756969.77905


i %N Years
41424344454647484950
133.499734.158134.810035.455536.094536.727237.353737.974038.588139.1961
31.927832.521333.107533.686434.258234.822935.380635.931536.475537.0129
30.459030.994131.521232.040632.552333.056533.553234.042634.524734.9997
29.085229.567830.042130.508230.966331.416531.858932.293832.721233.1412
227.799528.234828.661629.080029.490229.892330.286630.673131.052131.4236
26.595126.987927.372027.747728.115128.474428.825929.169529.505729.8344
25.466125.820626.166426.503826.833027.154227.467527.773228.071428.3623
24.406924.726925.038425.341525.636525.923626.203026.474926.739626.9972
323.412423.701423.981924.254324.518724.775425.024725.266725.501725.7298
22.477922.738922.991723.236523.473623.703223.925624.141124.349724.5518
21.599121.834922.062722.282822.495522.700922.899423.091223.276623.4556
20.772020.985121.190521.388421.579221.763121.940322.111122.275822.4345
41424344454647484950
419.993120.185620.370820.548820.720020.884721.042921.195121.341521.4822
19.258819.432919.599919.760119.913720.061120.202520.338220.468320.5931
18.566118.723518.874219.018419.156319.288419.414719.535619.651319.7620
17.912218.054618.190518.320318.444218.562518.675418.783218.886118.9844
517.294417.423217.545917.662817.774117.880117.981018.077218.168718.2559
16.710216.826816.937617.042817.142817.237817.328117.413917.495417.5728
16.157516.263016.363016.457916.547716.632916.713716.790216.862816.9315
15.634015.729615.819915.905415.986216.062616.134816.203116.267816.3288
615.138015.224515.306215.383215.455815.524415.589015.650015.707615.7619
14.667614.746014.819714.889214.954515.016015.073915.128415.179615.2279
14.221214.292214.358814.421414.480214.535414.587314.635914.681614.7245
13.797113.861513.921813.978214.031114.080714.127114.170614.211314.2495
41424344454647484950
713.394113.452413.507013.557913.605513.650013.691613.730513.766813.8007
13.010813.063713.113013.159013.201813.241813.279113.313813.346213.3764
12.646012.693912.738512.780012.818612.854512.887912.919012.947912.9748
12.298512.342012.382312.419812.454612.486812.516812.544612.570412.5943
811.967212.006712.043212.077112.108412.137412.164312.189112.212212.2335
11.651311.687111.720211.750811.779011.805111.829211.851411.872011.8910
11.349811.382311.412311.439911.465311.488811.510411.530311.548711.5656
11.061811.091311.118411.143411.166311.187411.206811.224711.241111.2562
910.786610.813410.838010.860510.881210.900210.917610.933610.948210.9617
10.523310.547710.570010.590410.609010.626110.641710.656110.669210.6812
10.271510.293610.313810.332210.349010.364410.378510.391310.403010.4137
10.030310.050310.068710.085310.100510.114410.127010.138510.149010.1585
109.799149.817409.834009.849099.862819.875289.886629.896939.906309.91481


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