## Single Payment Present WorthSPPW

The SPPW factor is used to determine the present worth, P, that a future amount, S, will be at interest of i-percent, in n years. If S is known, and P is to be determined, then Equation 9-4 is used.

Time Periods

Figure 9-2. Single payment presentworth (SPRW)

Time Periods

Figure 9-2. Single payment presentworth (SPRW)

Table 9-1.10% Interest Factors.

Single-payment Compound-amount (SPC A)

Period

Future value of «1

Single-payment present-

worth (SPPW)

Uni forra -

aeries compound-amount

Sinking-fund payment (SFP)

Capital recovery

Present value

Future value of uniform

Uniform series whose future value is \$1

Uniform aeries ■with present value of II i(l + t)»

value of uniform series of \$1

Future value of «1

Present value

Future value of uniform

Uniform series whose future value is \$1

Uniform aeries ■with present value of II i(l + t)»

value of uniform series of \$1

Table 9-2. 12% Interest Factors.
 Period rt Single-payment compound-amount (SPCA) Siogle- payment present-worth (SPPW) Uniform-eeriea compound-HDiount (trscA) Sinking-fund payment
 Period n Single-payment compound-amount (SPCA) Single-payment present-worth (SPPW) UniformOeries compound-amount (USC A) Sinking-fund payment (SFP) Capital recovery scrim present-worth (UBPW) FutUre valut of 11 (1 + s» Present value of \$1 1 (1 + .!• Future value of uniform aerie . 11 i Uniform series whose future value is SI i series with present value of \$1 ,Y1 Of uniform . of il aenesi ¿(1 + (1 + 0" - 1 1 1.150 0,8696 1.000 1,00000 1.15000 0.870 2 1.322 0.7561 2.150 0.46512 0.61512 1.626 3 1.521 0.6575 3.472 0.28798 0.43798 2.283 4 1.749 0.5718 4.983 0.20027 0,36027 2.855 5 2.011 0.48'2 6.742 0.14812 0.28832 3.352 6 2.313 0.4323 8.754 0.11424 0.28424 3.784 7 2.660 0.3758 11.067 0.09036 0.24036 4.160 8 3.059 0.3269 13.727 0.07285 0.22285 4.487 9 3.518 0.2843 16.786 0.05957 0.20857 4.772 10 4.046 0.2472 20.304 0.04925 0.18925 5.019 11 4.652 0.2149 24.349 0.04107 0.19107 5.234 12 5.350 0.1869 29.002 0.03448 0.18448 5.421 13 8.153 0.1625 34.352 0.02911 0.17811 5.583 14 7.076 0.1413 40.605 0.02469 0.17469 5.724 15 8.137 0.1229 47.580 0.02102 0.17102 5.847 16 s.ass 0.1069 65.717 0.01795 0.16795 5.954 17 10.761 0.0928 65.075 0.01537 0.16537 6.047 18 12.375 0.0808 75.836 0.01319 0.16318 6.128 19 14.232 0.0703 88.212 0.01134 0.16134 6.198 20 16.367 0.06U 102.444 0.00876 0.15976 6.259 21 18.822 0.0531 118.810 0.00842 0.15842 6.312 22 21.645 0.0462 137.632 0.00727 0.15727 6.358 23 24.891 0.0402 159.276 0.00628 0.15628 6.398 24 28.625 0.0348 184.168 0.00543 0.15543 6.434 25 32.919 0.0304 212.783 0.00470 0.15470 6.464 26 37.867 0.0264 245.712 0.00407 0.15407 6.491 27 43.535 0.0230 283.569 0.00353 0.15353 6.514 28 50.066 0.0200 327,104 0.00306 0.15306 6.534 29 57.575 0.0174 377.170 0.00265 0.15265 6.551 30 66.212 0.0151 434.745 0.00230 0.15230 6.566 35 133.176 0.0075 881.170 0.00113 0.15113 6.617 40 267,864 0.0037 1779. OW 0.00056 0.15056 6.642 45 538.768 0.0018 3585.128 0.00028 0.15028 6.654 50 1083.657 0.0000 7217.716 0.00014 0.15014 6.661 55 2178.622 0.0005 14524.148 0.00007 0.15007 6.664 60 4381.998 0.0002 29219.992 0.00003 0.15003 6.665 85 8817.787 0.0001 58778.583 0.00002 0.15002 6.666

Table 9-4. 20% Interest Factors.

Period

Single-

payment compound-amount (SPCA)

5ingle~

payment present-

worth <SPPW>

Present value *1

Uniform-

series compound-amount (TJSCA)

Future value cf uniform series of

Sinking-fund payment (SFP)

Uniform aeries whose future value is 11

Capital recovery

Uniform-

series uresent-

worth (USFW)

Uniform-

series uresent-

worth (USFW)

Uniform series with present value of tl

oMimform aeries cf II (1 +i)> - 1 ¿(1 + •)■

11 12

18 17 IS

35 40 45 50

7.430 8.916 10.699 12.839 15.407

18.488 22.186 26.623 a1.948 38.338

46.005

55.206 66.247 79.497 95.396

114.475 137.371 164.846 197.814 237.376

590.668 1469.772 3657.262 9100.438

0.8333

0.8944 0.5787 0.4823 0.4019

0.3349 0.2791 0.2326 0.1938 0.1615

0.1346 0.1122 0.0935 0.0779 0.0649

0.0541 0.0451 0 0379 0.0313

0.0261

0.0217 0.0181 0.0151 0.0126 0.0105

0.0087 0.0073 0.0061 0.0051 0.0042

0.0017 0.0007

0.0003 0.0001

9.930 12.916 16.499 20.799 25.959

32.150 39.581 48.497 59.196 72.035

87.442 105.931 128.117 154.740 186,688

225.026 271.031 326.237 392.484 471.981

587.377 681.853 819.223 984.068 1181.882

2948.341 7343.858 18281.310 45497.191

l.OOOOO

0.45455 0.27473 0.18629 0.13438

0.10071 0.07742 0.06061 0.04808 0.03852

0.03110 0.02526 0.02062 0,01689 0.01388

0.01144 0.00944

0.00781 0.00646

0.00536

0.00444 0.00369 0.00307 0.00255 0.00212

0.00176 0.00147 0.00122 0.00102 0.00085

0.00034 0.00014 0.00005 0.00002

3.30000 0.65455 0.47473 0.38629 0.33438

0.30071 0.27742 0.26061 0 21808 0.23852

0.23110 0.22526 0.22062 a 21G8B 0.21388

0.21144 0.20944 0.20781 0.20646 0.20536

0.20444

0.20369 0.20307 0.20256 0.20212

0.20170 0.20147 0.20122 0.20102 0.20085

0.20034 0.20014 0 2000/> 0.20002

2.991

Table 9-5. 25% Interest Factors.

Period

Single-payment compound-amount

Single-

payment present-

worth <SPPW>

Uniform-

series compound amount (ÜSCA)

Sinking-fund payment (SFP)

Capital recovery (CR)

Uniform-

series present-

worth {USPW)

11 12

17 IB

35 40

Present velue t MO 1 362

1 953

2 441 3.052

3 815

11 642 14.552 18 190 22.737 28.422

108.420 135.525 169,407 211.758 264.698

330.872 413.590 516 988 640.235 807 7 94

24B5 190 7523 164

0 8000 0.6400 0,5120 0 4096 0.3277

0.2621 0.2097 0 1678 0.1342 0.1074

0.0859 0.0687 0.0550 0.0440 0.0352

0.0281 0 0225 0.0180 0.0144 0.0115

0 0092 0.0074 0 0059 0.0047

0.0038

0.0004 O 0001

Future value of uniform Aeries of

Uniform aeriea future value ia II i

Uniform aeries

^ftra*1 id

Present value of uniform serie? tl (1 +-■>" - 1

11.259 15,073 19.842 25.802

33.253

42,560 54.208 68,7W 86.949 109.687

138. 109 173.636 218 045 273 556 342.945

429.681 538.101 673.626 843.033 1054.791

1319,480

1650.361 2063 952 2580.939 3227.1T4

9856.T61 30088.655

1 00000 0.44444 0.26230 0.17344 0.12185

0.08882 0.06634 0.05040 0.03876 0 03007

0 02349 0.01845 0.01454 0.01150 0.00912

0.00724 0.00576 0 00459 0 00366 0.00292

0.00233 0.00186 0 00148 000119 0,00095

0.00076 0.00061 0 00048 0.00039 0.00031

o.oooio

0.00003

1.25000 O 69444 0.51230 0.42344 0.37185

0.33882 0.31634 0.30040 0 28876 0 28007

0 27349 0 26845 0.28454 O 26150 0.25912

0.25724

0.25576 0 25459 0.25366 0.25292

0.25233 0 25186 0 25148 0 25119 0.25095

0.25076 0.25061 0.25048 0.25039 0.25031

0.25010

0.25003

0 800 1.440 1.952

2 362 2.689

2.951 3.161 3.329

3 463 3.571

3.933 3.990

3.992

3.994

3.995

3.998

3.999

Table 9-6.30% Interest Factors.

Period

14 16

16 17

21 22

Single-

payment compound-amount (SPCA)

4.827 8,275 8.167 10 604 13.780

17.922 23 203 30.288 39 374 51.1SS

66 542 86 504 112 455 146.192 190 050

247 065 321 184 417.539 542 801 705.641

9 IT.333 1192.533 1550.293 2015 381 2619.996

9727.860

Single-payment present-worth (SPPW)

Preaofi^ value 1

0.7692 0,5917 0.4552 0.350L 0,2693

0.2072 0.1594 0.1220 0.0943 0.0725

0.0558 0.0429 0.0330 0.0254 0.0195

0.0150 0.0116 O.OOS9 0.0068 0,0053

0.0040 0 0031 0.0024 0.0018 0.0014

O.OOlt o 0008 0.0006 0.0005 0.0004

0,0001

Uniform-

series comp o und-

amount (USCA)

value of uniform series of 11

1 000

12 756 17 583 23 858 32.015 42.619

56.405 74.327 97 625 127.913 167.286

218.472 285.014 371.518 483.973 630.165

820.215 1067.280 1388.464 1806.003 2348.803

3054.444 3971.778 5164.311 6714.604 8729.985

32422.868

Sinkin=-fund payment (SFP)

Uniform series whose future value is \$1 i

l.oouoo

0.43478 0 25063 0.16163 0.11068

0 07839 O 05687 O 04192 0.03124 0.02346

0.01773 O 01345 0.01024 0.00782 0 00598

0.00458 0.00351 0.00269 0.00207 0.00159

0.00122 0,00094 0.00072 0.00055 0.00043

0.00033 0.00025

o 00019

0.00015 O 00011

0.00003

Capital recovery (CE)

Uniform serins present value cf II Hi + i)"

1.30000 0 73478 0.55063 0.46163 0 41058

0.37839 0 35687 0.34192 0,33124 0.32346

0 31773 0.31345 0.31024 0.30782 0.30598

0.30458 0.30351 0 30269 0.30207 0,30159

0 30122 0.30094 0.30072 0.30055 0.30043

0.30033 0.30025 0.30019

o.aooia

0.30011 0.30003

Uniform-

series present-

worth (USPW)

0.769

1 361 1 816

2.166

2 436

3.147 3.190 3.223

3 249 3.368

3.330

3.331

3.331

3.332

3.332

3.333

Single-

payment compound-amount (SPCA)

Single-payment present-worth (SPPW)

Uniform-

series comp o und-

amount (USCA)

Uniform-

series present-

worth (USPW)

9727.860

32422.868

3.333

 Period n Single-payment compound-nmount payment present- worth (SPPW) Uniform-»erie» compound-mount (USCA) Sinking-fund payment (HFP) aerie) present- worth (USPW) Future value of *1 (1 + x>" Pressp lvalue 1 Future value of uniform .aeries of IL, Uniform series ■whose future value is \$1 i Uniform . aorityi with present value of \$1 (a + 0- Present value of uniform series of (1 + tj« - 1 (1 + .')» 1 t)--' i + ■ 1 1.400 0.7143 1.000 1.00000 1.40000 0.l14 2 1.960 0.5102 2.400 0.41667 0.81667 1.224 3 2.744 0.3044 4.360 0.22836 0.62936 1.589 4 3.842 0.2003 7.104 O.14077 0.54077 1.848 5 5.378 0.1859 10.846 0.08136 0.48136 2.03S 6 7.530 0.1328 16.324 0.06128 0.46126 2.168 7 10.541 0.0949 23.83 0.04192 0.44182 2.263 8 14.758 0.0078 34.395 0.02807 0.42907 2.331 8 20.001 0.0484 48.153 0.02034 0.42034 2.3l9 10 28.925 0.0346 69.814 0.01432 0.41432 2.414 11 40.496 0.0247 9B.73B 0.01013 0.41013 2.438 12 56.694 0.0176 138.235 0.00718 0.40718 2.4S6 13 79.371 0.0126 195.828 0.00510 0.40510 2.469 14 111.120 0.0090 275.300 0.00363 0.40303 2.4l8 15 155.568 0.0064 386.420 0.00259 0.40259 2.484 16 217.785 0.0046 641.988 0.00185 0.40185 2.489 17 304.913 0.0033 758.784 0.00132 0.40132 2.492 18 426.879 0.0023 1064.697 0.00094 0.40094 2.494 19 587.630 0.0017 1481.576 0.00067 0.40067 2.486 20 836.683 0.0012 2088.206 0.00048 0.40048 2.48l 21 1171.358 0 0009 2925.889 0.00034 0,40034 2.498 22 1838.898 o.oooe 4087.245 0.00024 0.40024 2.498 23 2285.857 0,0004 5737.142 0.00017 0.40017 2.488 24 3214.200 0.0003 8032.988 0.00012 0.40012 2.498 25 4489.880 0.0002 11247.189 0.00009 0.40009 2.498 26 6289.831 0.O0O2 15747.079 0 00006 0.40006 2.S00 27 8819.764 0.0001 22046.910 o.oooos 0.40005 2.S00

Table 9-8. 50% Interest Factors.

Period

Single-payment compound-amount

Single-payment present-TV orth

Uniform-

aeries compound-amount fUSCA)

Sinking-fund psyment (SFP)

Capital recovery

Uniform-

eeriea preaent-worth (trSPW)

Present value of IL

Future value of uniform ,SerlW otil

Uniform eerie» future value is \$1

Uniform aeries with present value of II

Present value

Future value of uniform ,SerlW otil

 I 1.500 0 6667 1 000 1 00000 1 50000 0.867 2 2 250 0 4444 2 500 0.4 0 90000 1.111 3 3. 375 0 2963 4 750 0 21053 0 71053 1.407 4 5 062 0 1975 8 125 0 12308 0 62308 1.605 5 7 594 0 1317 13 188 0.07583 0 57583 1.737 0 11 391 0 0878 20 781 0 04812 0 54812 1.824 7 17 .086 0 0585 32 172 0 03108 0 53108 1.883 B 25 629 0 0390 49 258 0 02030 0 52030 1.922 9 3B 443 0 0260 74 .887 0 01335 0 51335 1.948 10 57 665 0 0173 113 330 0 00882 0 50882 1.965 11 B6 49B 0 0116 170 995 0 00585 0 50585 1.977 12 129 .746 0 0077 257 493 0 003% 0 50388 1.985 13 194 820 0 0051 387 239 0 00258 0 50258 1.99 14 291 92B 0 0034 581 859 0 00172 0 50172 1.993 15 437 B94 0 0023 873 .788 0 00114 0 50114 1.995 IS 656 B41 15 1311 682 0 00076 0.50076 1.997 17 BB5 261 0 0010 1968 523 0 00051 0 50051 1.998 1B 1477 .892 0 0007 2953 .784 0 00034 0 50034 1.999 19 221B B3B 0 0005 4431 676 0 00023 0 50023 1.999 20 3325 .257 0 0003 8648 513 0 00015 0 50015 1.999 21 49B7 .885 0.0002 9973 ,770 0 00010 0 50010 2 22 74B1 .828 0 0001 14961 655 0 00007 0.50007 2

Present value of IL

Table 9-9. Five-Year Escalation Table.

Present Worth of a Series of Escalating Payments Compounded Annually Discount-EscalationFactors for n = 5 Years

Discount Rate

0.10

0.12

Annual Escalation Rate

0.14

0.16

o.is

0.20

0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34

5.000000 4.866862 4.738562 4.615647 4.497670 4.384494 4.275647 4.171042 4.070432 3.973684 3.880510 3.790801 4.704368 3.621094 3.540773 3.463301 3.388553 3.316408 3.246718 3.179393 3.114338 3.051452 2.990618 2.931764 2.874812

5.279234 5.136200 5.000000 4.869164 4.742953 4.622149 4.505953 4.394428 4,287089 4.183921 4.084577 3.989001 3.896891 3.808179 3.722628 3.640161 3.560586 3.483803 3.409649 3.338051 3.268861 3.201978 3.137327 3.074780 3.014281

5.572605 5.420152 5.274242 5.133876 5.000000 4.871228 4.747390 4.628438 4.513947 4.403996 4.298207 4.196400 4.098287 4.003835 3.912807 3.825008 3.740376 3.658706 3.579870 3.503722 3.430201 3.359143 3.290436 3.224015 3.159770

5,880105 5.717603 5.561868 5.412404 5.269208 5.131703 5.000000 4.873699 4.751566 4.634350 4.521178 4.413341 4.308947 4.208479 4.111612 4.018249 3.928286 3.841442 3.757639 3.676771 3.598653 3.523171 3.450224 3.379722 3,311524

6.202627 6.029313 5.863289 5.704137 5.551563 5.404955 5.264441 5.129353 5.000000 4.875619 4.755725 4,640260 4.529298 4.422339 4.319417 4.220158 4.124553 4.032275 3.943295 3.857370 3.774459 3,694328 3.616936 3.542100 3.469775

6.540569 6.355882 6.179066 6.009541 5.847029 5.691165 5.541511 5.397964 5.259749 5.126925 5.000000 4.877689 4.759649 4.645864 4.536517 4.431144 4.329514 4.231583 4.137057 4.045902 3.957921 3.872901 3.790808 3.711472 3.634758

Table 9-10. Ten-Year Escalation Table.

Resent VCcth of a Series of Escalating Payments Compounded Annually Discount-EscalationFactors for n = 10 Years

Discount Rate

0.10

0.12

0.14

0.16

0.18

0.20

0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0,25 0.26 0.27 0,28 0.29 0.30 0.31 0.32 0.33 0,34

10.000000 9.518405 9.068870 8.650280 8,259741 7.895187 7,554141 7.234974 6.935890 6.655455 6.392080 6.144593 5.911755 5.692557 5.485921 5.290990 5,106956 4.933045 4.768518 4.612762 4.465205 4.325286 4.192478 4.066339 3.946452

11.056250 10.508020 10,000000 9,526666 9.084209 8.672058 8.286779 7.926784 7.589595 7.273785 6.977461 6.699373 6.437922 6.192047 5.960481 5.742294 5.536463 5.342146 5.158489 4.984826 4.820429 4.664669 4.517015 4.376884 4.243845

12.234870 11.613440 11.036530 10.498990 10.000000 9.534301 9.099380 8.693151 8.312960 7,957330 7.624072 7.311519 7.017915 6.742093 6.482632 6.238276 6.008083 5.790929 5.585917 5.392166 5.209000 5.035615 4,871346 4.715648 4,567942

13,548650 12.844310 12.190470 11.582430 11.017130 10.490510 10.000000 9.54 2653 9.113885 8.713262 8.338518 7.987156 7.657542 7.348193 7.057347 6.783767 6.526298 6.283557 6.054608 5.838531 5.634354 5.441257 5.258512 5.085461 4.921409

15.013550 14.215140 13.474590 12.786980 12.147890 11.552670 10.998720 10.481740 10.000000 9.549790 9.128122 8.733109 8.363208 8.015993 7.690163 7.383800 7.095769 6.824442 6.568835 6.327682 6.100129 5.885058 5.681746 5.489304 5.307107

16.646080 15.741560 14.903510 14.L25780 13.403480 12.731900 12.106600 11.524400 10.980620 10.472990 10,000000 9.557141 9.141752 8.752133 8.387045 8.044173 7.721807 7.418647 7.133100 6.864109 6.610435 6.370867 6.144601 5.930659 5.728189

Resent VCcth of a Series of Escalating Payments Compounded Annually Discount-EscalationFactors for n = 10 Years

Discount Rate

0.16

0.18

0.20

Table 9-11. Fifteen-Year Escalation Table.

Resent Worth of a Series of Escalating Payments Compounded Annually Discount-Escalation Factors for n = 15 years

Discount Rate

Annual Escalation Rate

0.10

0.12

0.14

0.16

0.18

0.20

0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0,23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34

15.000000 13.964150 13.026090 12.177030 11.406510 10.706220 10.068030 9.485654 8.953083 8.465335 8.017635 7.606115 7.227109 6.877548 6.554501 6.25551B 5.978393 5.721101 5.481814 5.258970 5.051153 4.857052 4.675478 4.505413 4.345926

17.377880 16.126230 15.000000 13.981710 13,057790 12.220570 11.459170 10.766180 10.133630 9.555676 9.026333 8.540965 6.094845 7.684317 7.305762 6.956243 6.632936 6.333429 6.05J485 5.797236 5.556882 5.332839 5.123753 4.928297 4.745399

20.199780 18.690120 17.332040 16.105770 15.000000 13.998120 13.088900 12.262790 11.510270 10.824310 10.197550 9.623969 9.097863 8.614813 8,170423 7.760848 7.382943 7.033547 6.710042 6.410005 6.131433 5.872303 5.630905 5.405771 5.195502

23.549540 21.727370 20.090360 18.616160 17.287320 16.086500 15.000000 14.015480 13.118840 12.303300 11.560150 10.881130 10.259820 9.690559 9.167798 8.687104 8.244519 7.836080 7.458700 7.109541 6.785917 6.485500 6.206250 5.946 343 5.704048

27.529640 25.328490 23.355070 21.581750 19.985530 18.545150 17.244580 16.066830 15.000000 14.030830 13.148090 12.343120 11.608480 10.936240 10.320590 9.755424 9.236152 8.757889 8.316982 7.909701 7.533113 7.184156 6.860492 6.559743 6.280019

32.259620 29.601330 27.221890 25.087260 23.169060 21.442230 19.884420 18.477610 17.203010 16.047480 15.000000 14.046400 13.176250 12.381480 ] 1.655310 10.990130 10.379760 9.819020 9.302823 8.827153 8.388091 7.982019 7.606122 7.257569 6.933897

Table 9-12. Twenty-Year Escalation Table.

Present Worth of a Series of Escalating Payments Compounded Annually Discount-EscalationFactorsfor n - 20 Years

Discount Rate

Annual Escalation Rate

0.10

0.12

0.14

0.16

0.18

0.20

0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34

20.000000 18.213210 16.642370 15.259850 14.038630 12.957040 11.995640 11.138940 10.373120 9.686791 9.069737 8.513605 8.010912 7.555427 7.141531 6.764528 6.420316 6.105252 5.816151 5.550301 5.305312 5.079039 4.869585 4.675331 4.494838

24,295450 22.002090 20.000000 18.243100 16.694830 15.329770 14.121040 13.048560 12.093400 11.240870 10.477430 9.792256 9.175267 8,618459 8.U4476 7.657278 7.241402 6.862203 6.515563 6,198027 S.906440 5.638064 5.390575 5.161809 4,949990

29.722090 26.776150 24.210030 21.964990 20.000000 18.271200 16.746150 15.397670 14.201180 13.137510 12.188860 11.340570 10.579620 9.895583 9.278916 8.721467 8.216490 7.757722 7.339966 6.958601 6.609778 6.289875 5.995840 5.725066 5.475180

36.592170 32.799710 29.505400 26.634490 24.127100 21.929940 20.000000 18.300390 16.795710 15.463070 14.279470 13.224610 12.282120 11.438060 10.679810 9.997057 9.380883 8.823063 8.316995 7.856833 7.437339 7.054007 6.702967 6.380829 6.084525

45.308970 40,417480 36.181240 32.502270 29.298170 26.498510 24.047720 21.894660 20.000000 18.326720 16.844020 15.527270 14.355520 13.309280 12.373300 11.533310 10.778020 10.096710 9.480940 8.922847 8.416060 7.954518 7.533406 7.148198 6.795200

56.383330 50.067940 44.614710 39.891400 35.789680 32.218060 29.098950 26.369210 23.970940 21.860120 20.000000 18.353210 16.890730 15.589300 14.429370 13.392180 12.462340 11.626890 10.874120 10.194520 9,579437 9.021190 8.513612 8.050965 7.628322

Present Worth of a Series of Escalating Payments Compounded Annually Discount-EscalationFactorsfor n - 20 Years

Annual Escalation Rate

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## Productivity Without Pain

Being able to do little yet reap a lot is every individuals ideal work formula. Though not always possible there are some interesting ways this can be achieved to some level of satisfaction for all.

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