Solve 56000=A*1-(1+8,15%/12)^-48/frac{8*15%{12}}*(1+8.15%/12)

$$56000 = A \times \frac { 1 - ( 1 + \frac { 8,15 \% } { 12 } ) ^ { - 48 } } { \frac { 8 \cdot 15 \% } { 12 } } \times ( 1 + \frac { 8.15 \% } { 12 } )$$

Solve for A

$$A = \frac{1956101390616322117412285541769036465898665073277788669656569567441981203825224650987345392517229667668191918978526621190196549690853601851635675007052979919528783066938098971134724307685569016988045962060806400000}{97554585940579748799976578482490220227389188240419134692711705692867498720453149120589484519299259374006855195521865683174994272173330219799648922584978822883735009273997659520300174453916697600313650158298103} = 20051\frac{3.438792175760597 \times 10^{208}}{9.755458594057975 \times 10^{208}} \approx 20051.352499285$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12.

$$672000=12A\times \frac{1-\left(1+\frac{\frac{8.15}{100}}{12}\right)^{-48}}{\frac{8\times \frac{15}{100}}{12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Expand \frac{8.15}{100} by multiplying both numerator and the denominator by 100.

$$672000=12A\times \frac{1-\left(1+\frac{\frac{815}{10000}}{12}\right)^{-48}}{\frac{8\times \frac{15}{100}}{12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Reduce the fraction \frac{815}{10000} to lowest terms by extracting and canceling out 5.

$$672000=12A\times \frac{1-\left(1+\frac{\frac{163}{2000}}{12}\right)^{-48}}{\frac{8\times \frac{15}{100}}{12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Express \frac{\frac{163}{2000}}{12} as a single fraction.

$$672000=12A\times \frac{1-\left(1+\frac{163}{2000\times 12}\right)^{-48}}{\frac{8\times \frac{15}{100}}{12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Multiply 2000 and 12 to get 24000.

$$672000=12A\times \frac{1-\left(1+\frac{163}{24000}\right)^{-48}}{\frac{8\times \frac{15}{100}}{12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Add 1 and \frac{163}{24000} to get \frac{24163}{24000}.

$$672000=12A\times \frac{1-\left(\frac{24163}{24000}\right)^{-48}}{\frac{8\times \frac{15}{100}}{12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Calculate \frac{24163}{24000} to the power of -48 and get \frac{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}.

$$672000=12A\times \frac{1-\frac{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}}{\frac{8\times \frac{15}{100}}{12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Subtract \frac{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721} from 1 to get \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}.

$$672000=12A\times \frac{\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}}{\frac{8\times \frac{15}{100}}{12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$672000=12A\times \frac{\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}}{\frac{8\times \frac{3}{20}}{12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Multiply 8 and \frac{3}{20} to get \frac{6}{5}.

$$672000=12A\times \frac{\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}}{\frac{\frac{6}{5}}{12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Express \frac{\frac{6}{5}}{12} as a single fraction.

$$672000=12A\times \frac{\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}}{\frac{6}{5\times 12}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Multiply 5 and 12 to get 60.

$$672000=12A\times \frac{\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}}{\frac{6}{60}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Reduce the fraction \frac{6}{60} to lowest terms by extracting and canceling out 6.

$$672000=12A\times \frac{\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}}{\frac{1}{10}}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Divide \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721} by \frac{1}{10} by multiplying \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721} by the reciprocal of \frac{1}{10}.

$$672000=12A\times \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}\times 10\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Multiply \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721} and 10 to get \frac{6828821015840582415998360493774315415917243176829339428489819398500724910431720438441263916350948156180479863686530597822249599052133115385975424580948517601861450649179836166421012211774168832021955511080867210}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}.

$$672000=12A\times \frac{6828821015840582415998360493774315415917243176829339428489819398500724910431720438441263916350948156180479863686530597822249599052133115385975424580948517601861450649179836166421012211774168832021955511080867210}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Multiply 12 and \frac{6828821015840582415998360493774315415917243176829339428489819398500724910431720438441263916350948156180479863686530597822249599052133115385975424580948517601861450649179836166421012211774168832021955511080867210}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721} to get \frac{81945852190086988991980325925291784991006918121952073141877832782008698925180645261295166996211377874165758364238367173866995188625597384631705094971382211222337407790158033997052146541290025984263466132970406520}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}.

$$672000=\frac{81945852190086988991980325925291784991006918121952073141877832782008698925180645261295166996211377874165758364238367173866995188625597384631705094971382211222337407790158033997052146541290025984263466132970406520}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}A\left(1+\frac{\frac{8.15}{100}}{12}\right)$$

Expand \frac{8.15}{100} by multiplying both numerator and the denominator by 100.

$$672000=\frac{81945852190086988991980325925291784991006918121952073141877832782008698925180645261295166996211377874165758364238367173866995188625597384631705094971382211222337407790158033997052146541290025984263466132970406520}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}A\left(1+\frac{\frac{815}{10000}}{12}\right)$$

Reduce the fraction \frac{815}{10000} to lowest terms by extracting and canceling out 5.

$$672000=\frac{81945852190086988991980325925291784991006918121952073141877832782008698925180645261295166996211377874165758364238367173866995188625597384631705094971382211222337407790158033997052146541290025984263466132970406520}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}A\left(1+\frac{\frac{163}{2000}}{12}\right)$$

Express \frac{\frac{163}{2000}}{12} as a single fraction.

$$672000=\frac{81945852190086988991980325925291784991006918121952073141877832782008698925180645261295166996211377874165758364238367173866995188625597384631705094971382211222337407790158033997052146541290025984263466132970406520}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}A\left(1+\frac{163}{2000\times 12}\right)$$

Multiply 2000 and 12 to get 24000.

$$672000=\frac{81945852190086988991980325925291784991006918121952073141877832782008698925180645261295166996211377874165758364238367173866995188625597384631705094971382211222337407790158033997052146541290025984263466132970406520}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}A\left(1+\frac{163}{24000}\right)$$

Add 1 and \frac{163}{24000} to get \frac{24163}{24000}.

$$672000=\frac{81945852190086988991980325925291784991006918121952073141877832782008698925180645261295166996211377874165758364238367173866995188625597384631705094971382211222337407790158033997052146541290025984263466132970406520}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}A\times \frac{24163}{24000}$$

Multiply \frac{81945852190086988991980325925291784991006918121952073141877832782008698925180645261295166996211377874165758364238367173866995188625597384631705094971382211222337407790158033997052146541290025984263466132970406520}{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721} and \frac{24163}{24000} to get \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{20376056152253355389711307726760796519777761179976965308922599660853970873179423447784847838721142371543665822692985637397880725946391685954538281323468540828424823613938530949320044871724677260292145438133400}.

$$672000=\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{20376056152253355389711307726760796519777761179976965308922599660853970873179423447784847838721142371543665822692985637397880725946391685954538281323468540828424823613938530949320044871724677260292145438133400}A$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{20376056152253355389711307726760796519777761179976965308922599660853970873179423447784847838721142371543665822692985637397880725946391685954538281323468540828424823613938530949320044871724677260292145438133400}A=672000$$

Multiply both sides by \frac{20376056152253355389711307726760796519777761179976965308922599660853970873179423447784847838721142371543665822692985637397880725946391685954538281323468540828424823613938530949320044871724677260292145438133400}{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}, the reciprocal of \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{20376056152253355389711307726760796519777761179976965308922599660853970873179423447784847838721142371543665822692985637397880725946391685954538281323468540828424823613938530949320044871724677260292145438133400}.

$$A=672000\times \frac{20376056152253355389711307726760796519777761179976965308922599660853970873179423447784847838721142371543665822692985637397880725946391685954538281323468540828424823613938530949320044871724677260292145438133400}{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}$$

Multiply 672000 and \frac{20376056152253355389711307726760796519777761179976965308922599660853970873179423447784847838721142371543665822692985637397880725946391685954538281323468540828424823613938530949320044871724677260292145438133400}{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721} to get \frac{1956101390616322117412285541769036465898665073277788669656569567441981203825224650987345392517229667668191918978526621190196549690853601851635675007052979919528783066938098971134724307685569016988045962060806400000}{97554585940579748799976578482490220227389188240419134692711705692867498720453149120589484519299259374006855195521865683174994272173330219799648922584978822883735009273997659520300174453916697600313650158298103}.

$$A=\frac{1956101390616322117412285541769036465898665073277788669656569567441981203825224650987345392517229667668191918978526621190196549690853601851635675007052979919528783066938098971134724307685569016988045962060806400000}{97554585940579748799976578482490220227389188240419134692711705692867498720453149120589484519299259374006855195521865683174994272173330219799648922584978822883735009273997659520300174453916697600313650158298103}$$