c# - Excel 中的 IRR 计算与 .NET IRR 计算

Question

我正在尝试在 .NET 应用程序中计算 IRR。该应用程序基于一个 Excel 工作表，该工作表也计算 IRR。.NET 应用程序调用 Microsoft.VisualBasic 命名空间中的 IRR 函数，而 Excel 文件使用内置的 IRR 函数。

通常，给定相同的输入，这两个函数会产生不同的结果。一个例子是初始投资为 68000（所以 -68000），然后 360 收到 500 的付款，Excel 产生 8.3% 的内部收益率。.NET 版本只会抛出一个无效参数异常。这意味着它们显然是 IRR 的不同实现，但是有没有办法在不安装 Excel 的情况下在服务器上获取 Excel 计算。或者是否有可能找出 .NET 版本和 Excel 产生不同结果的原因？

需要明确的是，对于这些相同的输入，数字或 IRR 计算器会失败。事实上，Excel 是我见过的唯一一个返回值的。

示例代码非常简单：IRR = Microsoft.VisualBasic.Financial.IRR(ref cashFlowArray)

根据文档，这个函数和 Excel 一样，使用 0.1 或 10% 的默认猜测值。

同样，失败的一个值是 -68000 的初始投资和 360 收到的 500 付款。因此 cashFlowArray 有 361 个值。-68000，然后是 360 个 500 的值。再次注意，这个数组在许多 IRR 计算器中都失败了，但在 Excel 中没有。

Answer 1

使用 3% 代码的猜测会报告 IRR 值，并且使用默认的 10% 猜测率，代码无法找到 IRR 猜测 = 3% nper = 360 pmt = 500 pv = -68000 fv = 0 type = 0

PV + PMT pvifa(i%, NPER) FV pvif(i%, NPER) = 0

f(i) = -68000 + 500 pvifa(i%, 360) + 0 pvif(i%, 360)

f'(i) = 0 + 500 pvifa'(i%, 360) + 0 pvif'(i%, 360)

i0 = 0.03
f(i1) = -51333.7319
f'(i1) = -555402.9838
i1 = 0.03 - -51333.7319/-555402.9838 = -0.0624261002332
Error Bound = |-0.0624261002332 - 0.03| = 0.092426 > 0.000001

i1 = -0.0624261002332
f(i2) = 9.58562829595E+13
f'(i2) = -3.52703952905E+16
i2 = -0.0624261002332 - 9.58562829595E+13/-3.52703952905E+16 = -0.0597083455222
Error Bound = |-0.0597083455222 - -0.0624261002332| = 0.002718 > 0.000001

i2 = -0.0597083455222
f(i3) = 3.53513174812E+13
f'(i3) = -1.29425364707E+16
i3 = -0.0597083455222 - 3.53513174812E+13/-1.29425364707E+16 = -0.0569769398537
Error Bound = |-0.0569769398537 - -0.0597083455222| = 0.002731 > 0.000001

i3 = -0.0569769398537
f(i4) = 1.30388189029E+13
f'(i4) = -4.7487384444E+15
i4 = -0.0569769398537 - 1.30388189029E+13/-4.7487384444E+15 = -0.0542311961039
Error Bound = |-0.0542311961039 - -0.0569769398537| = 0.002746 > 0.000001

i4 = -0.0542311961039
f(i5) = 4.80979209853E+12
f'(i5) = -1.74212182057E+15
i5 = -0.0542311961039 - 4.80979209853E+12/-1.74212182057E+15 = -0.051470314493
Error Bound = |-0.051470314493 - -0.0542311961039| = 0.002761 > 0.000001

i5 = -0.051470314493
f(i6) = 1.77451366501E+12
f'(i6) = -6.39013222467E+14
i6 = -0.051470314493 - 1.77451366501E+12/-6.39013222467E+14 = -0.0486933552648
Error Bound = |-0.0486933552648 - -0.051470314493| = 0.002777 > 0.000001

i6 = -0.0486933552648
f(i7) = 654801046907
f'(i7) = -2.34346900134E+14
i7 = -0.0486933552648 - 654801046907/-2.34346900134E+14 = -0.045899202466
Error Bound = |-0.045899202466 - -0.0486933552648| = 0.002794 > 0.000001

i7 = -0.045899202466
f(i8) = 241674888932
f'(i8) = -8.59231252001E+13
i8 = -0.045899202466 - 241674888932/-8.59231252001E+13 = -0.0430865150973
Error Bound = |-0.0430865150973 - -0.045899202466| = 0.002813 > 0.000001

i8 = -0.0430865150973
f(i9) = 89220641583.2
f'(i9) = -3.14949542075E+13
i9 = -0.0430865150973 - 89220641583.2/-3.14949542075E+13 = -0.0402536599994
Error Bound = |-0.0402536599994 - -0.0430865150973| = 0.002833 > 0.000001

i9 = -0.0402536599994
f(i10) = 32948550352.8
f'(i10) = -1.15404773652E+13
i10 = -0.0402536599994 - 32948550352.8/-1.15404773652E+13 = -0.037398617759
Error Bound = |-0.037398617759 - -0.0402536599994| = 0.002855 > 0.000001

i10 = -0.037398617759
f(i11) = 12172461316.1
f'(i11) = -4.22688689595E+12
i11 = -0.037398617759 - 12172461316.1/-4.22688689595E+12 = -0.0345188479388
Error Bound = |-0.0345188479388 - -0.037398617759| = 0.00288 > 0.000001

i11 = -0.0345188479388
f(i12) = 4499225447.44
f'(i12) = -1.54731871431E+12
i12 = -0.0345188479388 - 4499225447.44/-1.54731871431E+12 = -0.0316110918277
Error Bound = |-0.0316110918277 - -0.0345188479388| = 0.002908 > 0.000001

i12 = -0.0316110918277
f(i13) = 1664095774.73
f'(i13) = -566016277566
i13 = -0.0316110918277 - 1664095774.73/-566016277566 = -0.0286710778375
Error Bound = |-0.0286710778375 - -0.0316110918277| = 0.00294 > 0.000001

i13 = -0.0286710778375
f(i14) = 616013742.551
f'(i14) = -206854614870
i14 = -0.0286710778375 - 616013742.551/-206854614870 = -0.025693074456
Error Bound = |-0.025693074456 - -0.0286710778375| = 0.002978 > 0.000001

i14 = -0.025693074456
f(i15) = 228298641.501
f'(i15) = -75498905652.4
i15 = -0.025693074456 - 228298641.501/-75498905652.4 = -0.0226692075598
Error Bound = |-0.0226692075598 - -0.025693074456| = 0.003024 > 0.000001

i15 = -0.0226692075598
f(i16) = 84742799.6012
f'(i16) = -27506966538.3
i16 = -0.0226692075598 - 84742799.6012/-27506966538.3 = -0.0195884316595
Error Bound = |-0.0195884316595 - -0.0226692075598| = 0.003081 > 0.000001

i16 = -0.0195884316595
f(i17) = 31524635.1226
f'(i17) = -9997137561.74
i17 = -0.0195884316595 - 31524635.1226/-9997137561.74 = -0.0164350655157
Error Bound = |-0.0164350655157 - -0.0195884316595| = 0.003153 > 0.000001

i17 = -0.0164350655157
f(i18) = 11762137.4745
f'(i18) = -3621337958.43
i18 = -0.0164350655157 - 11762137.4745/-3621337958.43 = -0.0131870567384
Error Bound = |-0.0131870567384 - -0.0164350655157| = 0.003248 > 0.000001

i18 = -0.0131870567384
f(i19) = 4405166.3509
f'(i19) = -1306482610.91
i19 = -0.0131870567384 - 4405166.3509/-1306482610.91 = -0.00981528101468
Error Bound = |-0.00981528101468 - -0.0131870567384| = 0.003372 > 0.000001

i19 = -0.00981528101468
f(i20) = 1656180.741
f'(i20) = -469715487.172
i20 = -0.00981528101468 - 1656180.741/-469715487.172 = -0.00628935779897
Error Bound = |-0.00628935779897 - -0.00981528101468| = 0.003526 > 0.000001

i20 = -0.00628935779897
f(i21) = 623022.4818
f'(i21) = -169271793.287
i21 = -0.00628935779897 - 623022.4818/-169271793.287 = -0.00260875354856
Error Bound = |-0.00260875354856 - -0.00628935779897| = 0.003681 > 0.000001

i21 = -0.00260875354856
f(i22) = 231175.5102
f'(i22) = -62482428.7318
i22 = -0.00260875354856 - 231175.5102/-62482428.7318 = 0.00109109479166
Error Bound = |0.00109109479166 - -0.00260875354856| = 0.0037 > 0.000001

i22 = 0.00109109479166
f(i23) = 80789.857
f'(i23) = -25081343.6949
i23 = 0.00109109479166 - 80789.857/-25081343.6949 = 0.00431220837988
Error Bound = |0.00431220837988 - 0.00109109479166| = 0.003221 > 0.000001

i23 = 0.00431220837988
f(i24) = 23316.5384
f'(i24) = -12346358.6651
i24 = 0.00431220837988 - 23316.5384/-12346358.6651 = 0.00620074402528
Error Bound = |0.00620074402528 - 0.00431220837988| = 0.001889 > 0.000001

i24 = 0.00620074402528
f(i25) = 3924.6872
f'(i25) = -8482801.9524
i25 = 0.00620074402528 - 3924.6872/-8482801.9524 = 0.00666340804385
Error Bound = |0.00666340804385 - 0.00620074402528| = 0.000463 > 0.000001

i25 = 0.00666340804385
f(i26) = 167.0698
f'(i26) = -7773372.0518
i26 = 0.00666340804385 - 167.0698/-7773372.0518 = 0.00668490062717
Error Bound = |0.00668490062717 - 0.00666340804385| = 2.1E-5 > 0.000001

i26 = 0.00668490062717
f(i27) = 0.3348
f'(i27) = -7742239.1148
i27 = 0.00668490062717 - 0.3348/-7742239.1148 = 0.00668494387585
Error Bound = |0.00668494387585 - 0.00668490062717| = 0 < 0.000001

IRR = 0.6684944%
Annual IRR = 8.0219327%
APR = 8.3235488%

并且使用 10% 的猜测率，代码报告 #NUM 错误猜测 = 10% nper = 360 pmt = 500 pv = -68000 fv = 0 type = 0

PV + PMT pvifa(i%, NPER) FV pvif(i%, NPER) = 0

f(i) = -68000 + 500 pvifa(i%, 360) + 0 pvif(i%, 360)

f'(i) = 0 + 500 pvifa'(i%, 360) + 0 pvif'(i%, 360)

i0 = 0.1
f(i1) = -63000
f'(i1) = -50000
i1 = 0.1 - -63000/-50000 = -1.16
Error Bound = |-1.16 - 0.1| = 1.26 > 0.000001

i1 = -1.16
f(i2) = 1.41683167973E+289
f'(i2) = 3.18909268602E+292
i2 = -1.16 - 1.41683167973E+289/3.18909268602E+292 = -1.16044427422
Error Bound = |-1.16044427422 - -1.16| = 0.000444 > 0.000001

i2 = -1.16044427422
f(i3) = 5.21945815669E+288
f'(i3) = 1.17157598387E+292
i3 = -1.16044427422 - 5.21945815669E+288/1.17157598387E+292 = -1.16088978166
Error Bound = |-1.16088978166 - -1.16044427422| = 0.000446 > 0.000001

i3 = -1.16088978166
f(i4) = 1.92279321388E+288
f'(i4) = 4.30401504168E+291
i4 = -1.16088978166 - 1.92279321388E+288/4.30401504168E+291 = -1.16133652574
Error Bound = |-1.16133652574 - -1.16088978166| = 0.000447 > 0.000001

i4 = -1.16133652574
f(i5) = 7.0833669401E+287
f'(i5) = 1.58116466833E+291
i5 = -1.16133652574 - 7.0833669401E+287/1.58116466833E+291 = -1.16178450988
Error Bound = |-1.16178450988 - -1.16133652574| = 0.000448 > 0.000001

i5 = -1.16178450988
f(i6) = 2.60943749624E+287
f'(i6) = 5.80871974114E+290
i6 = -1.16178450988 - 2.60943749624E+287/5.80871974114E+290 = -1.16223373752
Error Bound = |-1.16223373752 - -1.16178450988| = 0.000449 > 0.000001

i6 = -1.16223373752
f(i7) = 9.6128918485E+286
f'(i7) = 2.13394757555E+290
i7 = -1.16223373752 - 9.6128918485E+286/2.13394757555E+290 = -1.16268421213
Error Bound = |-1.16268421213 - -1.16223373752| = 0.00045 > 0.000001

i7 = -1.16268421213
f(i8) = 3.5412877151E+286
f'(i8) = 7.83947662856E+289
i8 = -1.16268421213 - 3.5412877151E+286/7.83947662856E+289 = -1.16313593714
Error Bound = |-1.16313593714 - -1.16268421213| = 0.000452 > 0.000001

i8 = -1.16313593714
f(i9) = 1.30457294757E+286
f'(i9) = 2.8799861182E+289
i9 = -1.16313593714 - 1.30457294757E+286/2.8799861182E+289 = -1.16358891604
Error Bound = |-1.16358891604 - -1.16313593714| = 0.000453 > 0.000001

i9 = -1.16358891604
f(i10) = 4.80590877868E+285
f'(i10) = 1.05801961691E+289
i10 = -1.16358891604 - 4.80590877868E+285/1.05801961691E+289 = -1.16404315231
Error Bound = |-1.16404315231 - -1.16358891604| = 0.000454 > 0.000001

i10 = -1.16404315231
f(i11) = 1.77044596708E+285
f'(i11) = 3.88684343018E+288
i11 = -1.16404315231 - 1.77044596708E+285/3.88684343018E+288 = -1.16449864942
Error Bound = |-1.16449864942 - -1.16404315231| = 0.000455 > 0.000001

i11 = -1.16449864942
f(i12) = 6.52213568706E+284
f'(i12) = 1.42790848513E+288
i12 = -1.16449864942 - 6.52213568706E+284/1.42790848513E+288 = -1.16495541088
Error Bound = |-1.16495541088 - -1.16449864942| = 0.000457 > 0.000001

i12 = -1.16495541088
f(i13) = 2.40268579877E+284
f'(i13) = 5.24570305717E+287
i13 = -1.16495541088 - 2.40268579877E+284/5.24570305717E+287 = -1.1654134402
Error Bound = |-1.1654134402 - -1.16495541088| = 0.000458 > 0.000001

i13 = -1.1654134402
f(i14) = 8.85124031729E+283
f'(i14) = 1.9271123403E+287
i14 = -1.1654134402 - 8.85124031729E+283/1.9271123403E+287 = -1.1658727409
Error Bound = |-1.1658727409 - -1.1654134402| = 0.000459 > 0.000001

i14 = -1.1658727409
f(i15) = 3.26070329379E+283
f'(i15) = 7.07962677255E+286
i15 = -1.1658727409 - 3.26070329379E+283/7.07962677255E+286 = -1.16633331649
Error Bound = |-1.16633331649 - -1.1658727409| = 0.000461 > 0.000001

i15 = -1.16633331649
f(i16) = 1.2012085951E+283
f'(i16) = 2.60084035073E+286
i16 = -1.16633331649 - 1.2012085951E+283/2.60084035073E+286 = -1.16679517052
Error Bound = |-1.16679517052 - -1.16633331649| = 0.000462 > 0.000001

i16 = -1.16679517052
f(i17) = 4.4251253663E+282
f'(i17) = 9.55469936824E+285
i17 = -1.16679517052 - 4.4251253663E+282/9.55469936824E+285 = -1.16725830653
Error Bound = |-1.16725830653 - -1.16679517052| = 0.000463 > 0.000001

i17 = -1.16725830653
f(i18) = 1.63016935972E+282
f'(i18) = 3.51010703892E+285
i18 = -1.16725830653 - 1.63016935972E+282/3.51010703892E+285 = -1.16772272808
Error Bound = |-1.16772272808 - -1.16725830653| = 0.000464 > 0.000001

i18 = -1.16772272808
f(i19) = 6.00537140858E+281
f'(i19) = 1.28950697217E+285
i19 = -1.16772272808 - 6.00537140858E+281/1.28950697217E+285 = -1.16818843874
Error Bound = |-1.16818843874 - -1.16772272808| = 0.000466 > 0.000001

i19 = -1.16818843874
f(i20) = 2.21231527014E+281
f'(i20) = 4.73725791429E+284
i20 = -1.16818843874 - 2.21231527014E+281/4.73725791429E+284 = -1.16865544208
Error Bound = |-1.16865544208 - -1.16818843874| = 0.000467 > 0.000001

i20 = -1.16865544208
f(i21) = 8.14993530042E+280
f'(i21) = 1.74032502975E+284
i21 = -1.16865544208 - 8.14993530042E+280/1.74032502975E+284 = -1.16912374169
Error Bound = |-1.16912374169 - -1.16865544208| = 0.000468 > 0.000001

i21 = -1.16912374169
f(i22) = 3.00234989778E+280
f'(i22) = 6.39342689545E+283
i22 = -1.16912374169 - 3.00234989778E+280/6.39342689545E+283 = -1.16959334116
Error Bound = |-1.16959334116 - -1.16912374169| = 0.00047 > 0.000001

i22 = -1.16959334116
f(i23) = 1.10603392004E+280
f'(i23) = 2.34875134593E+283
i23 = -1.16959334116 - 1.10603392004E+280/2.34875134593E+283 = -1.1700642441
Error Bound = |-1.1700642441 - -1.16959334116| = 0.000471 > 0.000001

i23 = -1.1700642441
f(i24) = 4.07451186961E+279
f'(i24) = 8.62860088603E+282
i24 = -1.1700642441 - 4.07451186961E+279/8.62860088603E+282 = -1.17053645413
Error Bound = |-1.17053645413 - -1.1700642441| = 0.000472 > 0.000001

i24 = -1.17053645413
f(i25) = 1.50100703398E+279
f'(i25) = 3.16988656752E+282
i25 = -1.17053645413 - 1.50100703398E+279/3.16988656752E+282 = -1.17100997487
Error Bound = |-1.17100997487 - -1.17053645413| = 0.000474 > 0.000001

i25 = -1.17100997487
f(i26) = 5.52955098198E+278
f'(i26) = 1.16452029784E+282
i26 = -1.17100997487 - 5.52955098198E+278/1.16452029784E+282 = -1.17148480996
Error Bound = |-1.17148480996 - -1.17100997487| = 0.000475 > 0.000001

i26 = -1.17148480996
f(i27) = 2.03702802856E+278
f'(i27) = 4.27809480963E+281
i27 = -1.17148480996 - 2.03702802856E+278/4.27809480963E+281 = -1.17196096304
Error Bound = |-1.17196096304 - -1.17148480996| = 0.000476 > 0.000001

i27 = -1.17196096304
f(i28) = 7.50419553643E+277
f'(i28) = 1.57164244159E+281
i28 = -1.17196096304 - 7.50419553643E+277/1.57164244159E+281 = -1.17243843778
Error Bound = |-1.17243843778 - -1.17196096304| = 0.000477 > 0.000001

i28 = -1.17243843778
f(i29) = 2.76446616007E+277
f'(i29) = 5.77373826379E+280
i29 = -1.17243843778 - 2.76446616007E+277/5.77373826379E+280 = -1.17291723782
Error Bound = |-1.17291723782 - -1.17243843778| = 0.000479 > 0.000001

#NUM! Error

但是，如果我们将基础 IRR 方程从现值更改为未来值，我们使用默认比率 10% guess = 10% nper = 360 pmt = 500 pv = -68000 fv = 0 type = 0 得到 IRR

FV + PMT fvifa(i%, NPER) PV fvif(i%, NPER) = 0

f(i) = 0 + 500 fvifa(i%, 360) + -68000 fvif(i%, 360)

f'(i) = 0 + 500 fvifa'(i%, 360) + -68000 fvif'(i%, 360)

i0 = 0.1
f(i1) = -5.02004033255E+19
f'(i1) = -1.64690644965E+22
i1 = 0.1 - -5.02004033255E+19/-1.64690644965E+22 = 0.0969518363756
Error Bound = |0.0969518363756 - 0.1| = 0.003048 > 0.000001

i1 = 0.0969518363756
f(i2) = -1.84406810006E+19
f'(i2) = -6.06751128825E+21
i2 = 0.0969518363756 - -1.84406810006E+19/-6.06751128825E+21 = 0.0939125868177
Error Bound = |0.0939125868177 - 0.0969518363756| = 0.003039 > 0.000001

i2 = 0.0939125868177
f(i3) = -6.77397490871E+18
f'(i3) = -2.23540131948E+21
i3 = 0.0939125868177 - -6.77397490871E+18/-2.23540131948E+21 = 0.0908822696886
Error Bound = |0.0908822696886 - 0.0939125868177| = 0.00303 > 0.000001

i3 = 0.0908822696886
f(i4) = -2.48832251727E+18
f'(i4) = -8.2357680071E+20
i4 = 0.0908822696886 - -2.48832251727E+18/-8.2357680071E+20 = 0.0878609090637
Error Bound = |0.0878609090637 - 0.0908822696886| = 0.003021 > 0.000001

i4 = 0.0878609090637
f(i5) = -9.14041085129E+17
f'(i5) = -3.03428884269E+20
i5 = 0.0878609090637 - -9.14041085129E+17/-3.03428884269E+20 = 0.084848535712
Error Bound = |0.084848535712 - 0.0878609090637| = 0.003012 > 0.000001

i5 = 0.084848535712
f(i6) = -3.35753185243E+17
f'(i6) = -1.11792988932E+20
i6 = 0.084848535712 - -3.35753185243E+17/-1.11792988932E+20 = 0.0818451882887
Error Bound = |0.0818451882887 - 0.084848535712| = 0.003003 > 0.000001

i6 = 0.0818451882887
f(i7) = -1.23330146611E+17
f'(i7) = -4.11886712617E+19
i7 = 0.0818451882887 - -1.23330146611E+17/-4.11886712617E+19 = 0.0788509147948
Error Bound = |0.0788509147948 - 0.0818451882887| = 0.002994 > 0.000001

i7 = 0.0788509147948
f(i8) = -4.53014608432E+16
f'(i8) = -1.51756548916E+19
i8 = 0.0788509147948 - -4.53014608432E+16/-1.51756548916E+19 = 0.075865774373
Error Bound = |0.075865774373 - 0.0788509147948| = 0.002985 > 0.000001

i8 = 0.075865774373
f(i9) = -1.66397969598E+16
f'(i9) = -5.59145206095E+18
i9 = 0.075865774373 - -1.66397969598E+16/-5.59145206095E+18 = 0.0728898395392
Error Bound = |0.0728898395392 - 0.075865774373| = 0.002976 > 0.000001

i9 = 0.0728898395392
f(i10) = -6.11188943532E+15
f'(i10) = -2.06020557437E+18
i10 = 0.0728898395392 - -6.11188943532E+15/-2.06020557437E+18 = 0.0699231989712
Error Bound = |0.0699231989712 - 0.0728898395392| = 0.002967 > 0.000001

i10 = 0.0699231989712
f(i11) = -2.244880032E+15
f'(i11) = -7.59113766115E+17
i11 = 0.0699231989712 - -2.244880032E+15/-7.59113766115E+17 = 0.0669659610285
Error Bound = |0.0669659610285 - 0.0699231989712| = 0.002957 > 0.000001

i11 = 0.0669659610285
f(i12) = -8.2451613754E+14
f'(i12) = -2.79714813418E+17
i12 = 0.0669659610285 - -8.2451613754E+14/-2.79714813418E+17 = 0.0640182582327
Error Bound = |0.0640182582327 - 0.0669659610285| = 0.002948 > 0.000001

i12 = 0.0640182582327
f(i13) = -3.02824717395E+14
f'(i13) = -1.03071538821E+17
i13 = 0.0640182582327 - -3.02824717395E+14/-1.03071538821E+17 = 0.0610802530291
Error Bound = |0.0610802530291 - 0.0640182582327| = 0.002938 > 0.000001

i13 = 0.0610802530291
f(i14) = -1.11215883952E+14
f'(i14) = -3.79821691345E+16
i14 = 0.0610802530291 - -1.11215883952E+14/-3.79821691345E+16 = 0.0581521452753
Error Bound = |0.0581521452753 - 0.0610802530291| = 0.002928 > 0.000001

i14 = 0.0581521452753
f(i15) = -4.08434211369E+13
f'(i15) = -1.3997236605E+16
i15 = 0.0581521452753 - -4.08434211369E+13/-1.3997236605E+16 = 0.055234182088
Error Bound = |0.055234182088 - 0.0581521452753| = 0.002918 > 0.000001

i15 = 0.055234182088
f(i16) = -1.49986675307E+13
f'(i16) = -5.15859333428E+15
i16 = 0.055234182088 - -1.49986675307E+13/-5.15859333428E+15 = 0.0523266709588
Error Bound = |0.0523266709588 - 0.055234182088| = 0.002908 > 0.000001

i16 = 0.0523266709588
f(i17) = -5.50747657445E+12
f'(i17) = -1.9013107922E+15
i17 = 0.0523266709588 - -5.50747657445E+12/-1.9013107922E+15 = 0.0494299974654
Error Bound = |0.0494299974654 - 0.0523266709588| = 0.002897 > 0.000001

i17 = 0.0494299974654
f(i18) = -2.02215465542E+12
f'(i18) = -7.00835643276E+14
i18 = 0.0494299974654 - -2.02215465542E+12/-7.00835643276E+14 = 0.0465446495599
Error Bound = |0.0465446495599 - 0.0494299974654| = 0.002885 > 0.000001

i18 = 0.0465446495599
f(i19) = -742382229633
f'(i19) = -2.58363859848E+14
i19 = 0.0465446495599 - -742382229633/-2.58363859848E+14 = 0.0436712514381
Error Bound = |0.0436712514381 - 0.0465446495599| = 0.002873 > 0.000001

i19 = 0.0436712514381
f(i20) = -272507455942
f'(i20) = -9.5261017302E+13
i20 = 0.0436712514381 - -272507455942/-9.5261017302E+13 = 0.0408106116542
Error Bound = |0.0408106116542 - 0.0436712514381| = 0.002861 > 0.000001

i20 = 0.0408106116542
f(i21) = -100010980524
f'(i21) = -3.5130785888E+13
i21 = 0.0408106116542 - -100010980524/-3.5130785888E+13 = 0.0379637928884
Error Bound = |0.0379637928884 - 0.0408106116542| = 0.002847 > 0.000001

i21 = 0.0379637928884
f(i22) = -36695132084.7
f'(i22) = -1.29592542042E+13
i22 = 0.0379637928884 - -36695132084.7/-1.29592542042E+13 = 0.0351322154298
Error Bound = |0.0351322154298 - 0.0379637928884| = 0.002832 > 0.000001

i22 = 0.0351322154298
f(i23) = -13459276157.9
f'(i23) = -4.78228823809E+12
i23 = 0.0351322154298 - -13459276157.9/-4.78228823809E+12 = 0.032317814564
Error Bound = |0.032317814564 - 0.0351322154298| = 0.002814 > 0.000001

i23 = 0.032317814564
f(i24) = -4934345607.23
f'(i24) = -1.76571704227E+12
i24 = 0.032317814564 - -4934345607.23/-1.76571704227E+12 = 0.0295232866249
Error Bound = |0.0295232866249 - 0.032317814564| = 0.002795 > 0.000001

i24 = 0.0295232866249
f(i25) = -1807771302.49
f'(i25) = -652436293382
i25 = 0.0295232866249 - -1807771302.49/-652436293382 = 0.0267524853668
Error Bound = |0.0267524853668 - 0.0295232866249| = 0.002771 > 0.000001

i25 = 0.0267524853668
f(i26) = -661642164.568
f'(i26) = -241351566265
i26 = 0.0267524853668 - -661642164.568/-241351566265 = 0.024011081303
Error Bound = |0.024011081303 - 0.0267524853668| = 0.002741 > 0.000001

i26 = 0.024011081303
f(i27) = -241789480.841
f'(i27) = -89439505964
i27 = 0.024011081303 - -241789480.841/-89439505964 = 0.0213076956097
Error Bound = |0.0213076956097 - 0.024011081303| = 0.002703 > 0.000001

i27 = 0.0213076956097
f(i28) = -88143000.1694
f'(i28) = -33239175916.2
i28 = 0.0213076956097 - -88143000.1694/-33239175916.2 = 0.0186559150604
Error Bound = |0.0186559150604 - 0.0213076956097| = 0.002652 > 0.000001

i28 = 0.0186559150604
f(i29) = -32000226.923
f'(i29) = -12413104775.8
i29 = 0.0186559150604 - -32000226.923/-12413104775.8 = 0.0160779760595
Error Bound = |0.0160779760595 - 0.0186559150604| = 0.002578 > 0.000001

i29 = 0.0160779760595
f(i30) = -11533230.93
f'(i30) = -4676205687.23
i30 = 0.0160779760595 - -11533230.93/-4676205687.23 = 0.0136116108692
Error Bound = |0.0136116108692 - 0.0160779760595| = 0.002466 > 0.000001

i30 = 0.0136116108692
f(i31) = -4099754.0982
f'(i31) = -1791032741.45
i31 = 0.0136116108692 - -4099754.0982/-1791032741.45 = 0.0113225661168
Error Bound = |0.0113225661168 - 0.0136116108692| = 0.002289 > 0.000001

i31 = 0.0113225661168
f(i32) = -1416951.762
f'(i32) = -709352254.433
i32 = 0.0113225661168 - -1416951.762/-709352254.433 = 0.00932503702855
Error Bound = |0.00932503702855 - 0.0113225661168| = 0.001998 > 0.000001

i32 = 0.00932503702855
f(i33) = -460027.8507
f'(i33) = -301702507.924
i33 = 0.00932503702855 - -460027.8507/-301702507.924 = 0.00780026398684
Error Bound = |0.00780026398684 - 0.00932503702855| = 0.001525 > 0.000001

i33 = 0.00780026398684
f(i34) = -128048.7026
f'(i34) = -149385114.618
i34 = 0.00780026398684 - -128048.7026/-149385114.618 = 0.00694309222036
Error Bound = |0.00694309222036 - 0.00780026398684| = 0.000857 > 0.000001

i34 = 0.00694309222036
f(i35) = -23557.3593
f'(i35) = -97513503.5079
i35 = 0.00694309222036 - -23557.3593/-97513503.5079 = 0.00670151173728
Error Bound = |0.00670151173728 - 0.00694309222036| = 0.000242 > 0.000001

i35 = 0.00670151173728
f(i36) = -1418.1361
f'(i36) = -85970536.3045
i36 = 0.00670151173728 - -1418.1361/-85970536.3045 = 0.00668501613117
Error Bound = |0.00668501613117 - 0.00670151173728| = 1.6E-5 > 0.000001

i36 = 0.00668501613117
f(i37) = -6.1578
f'(i37) = -85224810.8526
i37 = 0.00668501613117 - -6.1578/-85224810.8526 = 0.00668494387741
Error Bound = |0.00668494387741 - 0.00668501613117| = 0 < 0.000001

IRR = 0.6684944%
Annual IRR = 8.0219327%
APR = 8.3235488%