Solve 56000=A*1-(11+8.15%/12)^-48/frac{8.15%{12}}*(11+8.15%/12)

$$56000 = A \times \frac { 1 - ( 11 + \frac { 8.15 \% } { 12 } ) ^ { - 48 } } { \frac { 8.15 \% } { 12 } } \times ( 11 + \frac { 8.15 \% } { 12 } )$$

Solve for A

$$A = \frac{877528096493647577864786390188978654656875751818760703693231149083364674491224388102733582037571278506743099319923212929994318726682113531791027524678952073515643872324517629093381081855101638478399510974546395463602479251123946954476999942402460761406709768000}{25395536213195817825536324188375456655359801624419036387801418128114433906530588626574180834489295109792622754066771931773235015096026200361362095092218012335244635434362571259223797844663586122411201798594336050049476525680834268113004791387473843351827418103} = 34\frac{1.4079865244989753 \times 10^{259}}{2.5395536213195817 \times 10^{259}} \approx 34.554422837$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12.

$$672000=12A\times \frac{1-\left(11+\frac{\frac{8.15}{100}}{12}\right)^{-48}}{\frac{\frac{8.15}{100}}{12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

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

$$672000=12A\times \frac{1-\left(11+\frac{\frac{815}{10000}}{12}\right)^{-48}}{\frac{\frac{8.15}{100}}{12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

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

$$672000=12A\times \frac{1-\left(11+\frac{\frac{163}{2000}}{12}\right)^{-48}}{\frac{\frac{8.15}{100}}{12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

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

$$672000=12A\times \frac{1-\left(11+\frac{163}{2000\times 12}\right)^{-48}}{\frac{\frac{8.15}{100}}{12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

Multiply 2000 and 12 to get 24000.

$$672000=12A\times \frac{1-\left(11+\frac{163}{24000}\right)^{-48}}{\frac{\frac{8.15}{100}}{12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

Add 11 and \frac{163}{24000} to get \frac{264163}{24000}.

$$672000=12A\times \frac{1-\left(\frac{264163}{24000}\right)^{-48}}{\frac{\frac{8.15}{100}}{12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

Calculate \frac{264163}{24000} to the power of -48 and get \frac{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}.

$$672000=12A\times \frac{1-\frac{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}}{\frac{\frac{8.15}{100}}{12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

Subtract \frac{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721} from 1 to get \frac{177768753492370724778754269318628196587518611370933254714609926896801037345714120386019265841425065768548359278467403522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}.

$$672000=12A\times \frac{\frac{177768753492370724778754269318628196587518611370933254714609926896801037345714120386019265841425065768548359278467403522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}}{\frac{\frac{8.15}{100}}{12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

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

$$672000=12A\times \frac{\frac{177768753492370724778754269318628196587518611370933254714609926896801037345714120386019265841425065768548359278467403522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}}{\frac{\frac{815}{10000}}{12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

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

$$672000=12A\times \frac{\frac{177768753492370724778754269318628196587518611370933254714609926896801037345714120386019265841425065768548359278467403522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}}{\frac{\frac{163}{2000}}{12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

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

$$672000=12A\times \frac{\frac{177768753492370724778754269318628196587518611370933254714609926896801037345714120386019265841425065768548359278467403522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}}{\frac{163}{2000\times 12}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

Multiply 2000 and 12 to get 24000.

$$672000=12A\times \frac{\frac{177768753492370724778754269318628196587518611370933254714609926896801037345714120386019265841425065768548359278467403522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}}{\frac{163}{24000}}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

Divide \frac{177768753492370724778754269318628196587518611370933254714609926896801037345714120386019265841425065768548359278467403522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721} by \frac{163}{24000} by multiplying \frac{177768753492370724778754269318628196587518611370933254714609926896801037345714120386019265841425065768548359278467403522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721} by the reciprocal of \frac{163}{24000}.

$$672000=12A\times \frac{177768753492370724778754269318628196587518611370933254714609926896801037345714120386019265841425065768548359278467403522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}\times \frac{24000}{163}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

Multiply \frac{177768753492370724778754269318628196587518611370933254714609926896801037345714120386019265841425065768548359278467403522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721}{177768753492370724778754269318628196587518611370935033565732377327690845481307751560109211067324341751669307780405579522412645105672183402529534665645526086346712448040537998814566584912645102856878412590160352350346335679765839876791033539712316903462791926721} and \frac{24000}{163} to get \frac{4266450083816897394690102463647076718100446672902398113150638245523224896297138889264462380194201578445160622683217684537903482536132401660708831975492626072321098752972911971549598037903482468565081902163848456408312056314380157042984804953095605683107006241304000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523}.

$$672000=12A\times \frac{4266450083816897394690102463647076718100446672902398113150638245523224896297138889264462380194201578445160622683217684537903482536132401660708831975492626072321098752972911971549598037903482468565081902163848456408312056314380157042984804953095605683107006241304000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523}\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

Multiply 12 and \frac{4266450083816897394690102463647076718100446672902398113150638245523224896297138889264462380194201578445160622683217684537903482536132401660708831975492626072321098752972911971549598037903482468565081902163848456408312056314380157042984804953095605683107006241304000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523} to get \frac{51197401005802768736281229563764920617205360074828777357807658946278698755565666671173548562330418941341927472198612214454841790433588819928505983705911512867853185035674943658595176454841789622780982825966181476899744675772561884515817659437147268197284074895648000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523}.

$$672000=\frac{51197401005802768736281229563764920617205360074828777357807658946278698755565666671173548562330418941341927472198612214454841790433588819928505983705911512867853185035674943658595176454841789622780982825966181476899744675772561884515817659437147268197284074895648000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523}A\left(11+\frac{\frac{8.15}{100}}{12}\right)$$

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

$$672000=\frac{51197401005802768736281229563764920617205360074828777357807658946278698755565666671173548562330418941341927472198612214454841790433588819928505983705911512867853185035674943658595176454841789622780982825966181476899744675772561884515817659437147268197284074895648000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523}A\left(11+\frac{\frac{815}{10000}}{12}\right)$$

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

$$672000=\frac{51197401005802768736281229563764920617205360074828777357807658946278698755565666671173548562330418941341927472198612214454841790433588819928505983705911512867853185035674943658595176454841789622780982825966181476899744675772561884515817659437147268197284074895648000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523}A\left(11+\frac{\frac{163}{2000}}{12}\right)$$

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

$$672000=\frac{51197401005802768736281229563764920617205360074828777357807658946278698755565666671173548562330418941341927472198612214454841790433588819928505983705911512867853185035674943658595176454841789622780982825966181476899744675772561884515817659437147268197284074895648000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523}A\left(11+\frac{163}{2000\times 12}\right)$$

Multiply 2000 and 12 to get 24000.

$$672000=\frac{51197401005802768736281229563764920617205360074828777357807658946278698755565666671173548562330418941341927472198612214454841790433588819928505983705911512867853185035674943658595176454841789622780982825966181476899744675772561884515817659437147268197284074895648000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523}A\left(11+\frac{163}{24000}\right)$$

Add 11 and \frac{163}{24000} to get \frac{264163}{24000}.

$$672000=\frac{51197401005802768736281229563764920617205360074828777357807658946278698755565666671173548562330418941341927472198612214454841790433588819928505983705911512867853185035674943658595176454841789622780982825966181476899744675772561884515817659437147268197284074895648000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523}A\times \frac{264163}{24000}$$

Multiply \frac{51197401005802768736281229563764920617205360074828777357807658946278698755565666671173548562330418941341927472198612214454841790433588819928505983705911512867853185035674943658595176454841789622780982825966181476899744675772561884515817659437147268197284074895648000}{28976306819256428138936945898936396043765533653462410471214377504413607813453163504297801403973867705522097168206109462153261152224565894612314150500220752074514129030607693806774353340761151765671181252196137433106452715801831899916938466973107655264435084055523} and \frac{264163}{24000} to get \frac{2133225041908448697345051231823538359050223336451199056575319122761612448148569444632231190097100789222580311341608842268951741268066200830354415987746313036160549376486455985774799018951741234282540951081924228204156028157190078521492402476547802841553503120652}{109691012061705947233098298773622331832109468977345087961653893635420584311403048512841697754696409813342887414990401616249289840835264191473878440584869009189455484040564703636672635231887704809799938871818299432950309906390493369309624992800307595175838721}.

$$672000=\frac{2133225041908448697345051231823538359050223336451199056575319122761612448148569444632231190097100789222580311341608842268951741268066200830354415987746313036160549376486455985774799018951741234282540951081924228204156028157190078521492402476547802841553503120652}{109691012061705947233098298773622331832109468977345087961653893635420584311403048512841697754696409813342887414990401616249289840835264191473878440584869009189455484040564703636672635231887704809799938871818299432950309906390493369309624992800307595175838721}A$$

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

$$\frac{2133225041908448697345051231823538359050223336451199056575319122761612448148569444632231190097100789222580311341608842268951741268066200830354415987746313036160549376486455985774799018951741234282540951081924228204156028157190078521492402476547802841553503120652}{109691012061705947233098298773622331832109468977345087961653893635420584311403048512841697754696409813342887414990401616249289840835264191473878440584869009189455484040564703636672635231887704809799938871818299432950309906390493369309624992800307595175838721}A=672000$$

Multiply both sides by \frac{109691012061705947233098298773622331832109468977345087961653893635420584311403048512841697754696409813342887414990401616249289840835264191473878440584869009189455484040564703636672635231887704809799938871818299432950309906390493369309624992800307595175838721}{2133225041908448697345051231823538359050223336451199056575319122761612448148569444632231190097100789222580311341608842268951741268066200830354415987746313036160549376486455985774799018951741234282540951081924228204156028157190078521492402476547802841553503120652}, the reciprocal of \frac{2133225041908448697345051231823538359050223336451199056575319122761612448148569444632231190097100789222580311341608842268951741268066200830354415987746313036160549376486455985774799018951741234282540951081924228204156028157190078521492402476547802841553503120652}{109691012061705947233098298773622331832109468977345087961653893635420584311403048512841697754696409813342887414990401616249289840835264191473878440584869009189455484040564703636672635231887704809799938871818299432950309906390493369309624992800307595175838721}.

$$A=672000\times \frac{109691012061705947233098298773622331832109468977345087961653893635420584311403048512841697754696409813342887414990401616249289840835264191473878440584869009189455484040564703636672635231887704809799938871818299432950309906390493369309624992800307595175838721}{2133225041908448697345051231823538359050223336451199056575319122761612448148569444632231190097100789222580311341608842268951741268066200830354415987746313036160549376486455985774799018951741234282540951081924228204156028157190078521492402476547802841553503120652}$$

Multiply 672000 and \frac{109691012061705947233098298773622331832109468977345087961653893635420584311403048512841697754696409813342887414990401616249289840835264191473878440584869009189455484040564703636672635231887704809799938871818299432950309906390493369309624992800307595175838721}{2133225041908448697345051231823538359050223336451199056575319122761612448148569444632231190097100789222580311341608842268951741268066200830354415987746313036160549376486455985774799018951741234282540951081924228204156028157190078521492402476547802841553503120652} to get \frac{877528096493647577864786390188978654656875751818760703693231149083364674491224388102733582037571278506743099319923212929994318726682113531791027524678952073515643872324517629093381081855101638478399510974546395463602479251123946954476999942402460761406709768000}{25395536213195817825536324188375456655359801624419036387801418128114433906530588626574180834489295109792622754066771931773235015096026200361362095092218012335244635434362571259223797844663586122411201798594336050049476525680834268113004791387473843351827418103}.

$$A=\frac{877528096493647577864786390188978654656875751818760703693231149083364674491224388102733582037571278506743099319923212929994318726682113531791027524678952073515643872324517629093381081855101638478399510974546395463602479251123946954476999942402460761406709768000}{25395536213195817825536324188375456655359801624419036387801418128114433906530588626574180834489295109792622754066771931773235015096026200361362095092218012335244635434362571259223797844663586122411201798594336050049476525680834268113004791387473843351827418103}$$