Solve =10000(1+0.08/14)^48*0.08/14/(1+frac{0.08{18})^48-1}

$$= \frac { 10000 ( 1 + \frac { 0.08 } { 14 } ) ^ { 48 } \cdot \frac { 0.08 } { 14 } } { ( 1 + \frac { 0.08 } { 18 } ) ^ { 48 } - 1 }$$

Evaluate

$$\frac{140901564179851851863678345555776063622360233034359589059751760115268560651490417703026382076781364405058262704899294483332785104463193094405450277217894400}{444947989675330690346955090100013325888077772427841053017859521093097785741166825541953462250920662004615016497029487867414699200211612620929191714392587}\approx 316.669739946$$

Solution Steps

Expand \frac{0.08}{14} by multiplying both numerator and the denominator by 100.

$$\frac{10000\left(1+\frac{8}{1400}\right)^{48}\times \frac{0.08}{14}}{\left(1+\frac{0.08}{18}\right)^{48}-1}$$

Reduce the fraction \frac{8}{1400} to lowest terms by extracting and canceling out 8.

$$\frac{10000\left(1+\frac{1}{175}\right)^{48}\times \frac{0.08}{14}}{\left(1+\frac{0.08}{18}\right)^{48}-1}$$

Add 1 and \frac{1}{175} to get \frac{176}{175}.

$$\frac{10000\times \left(\frac{176}{175}\right)^{48}\times \frac{0.08}{14}}{\left(1+\frac{0.08}{18}\right)^{48}-1}$$

Calculate \frac{176}{175} to the power of 48 and get \frac{608987046553436365433244435090867457286274743288271182328020372539943012626226269251106032488147015251787776}{463261636424876129938368329678177489488710534372668564138134650863022623301645808169269002974033355712890625}.

$$\frac{10000\times \frac{608987046553436365433244435090867457286274743288271182328020372539943012626226269251106032488147015251787776}{463261636424876129938368329678177489488710534372668564138134650863022623301645808169269002974033355712890625}\times \frac{0.08}{14}}{\left(1+\frac{0.08}{18}\right)^{48}-1}$$

Multiply 10000 and \frac{608987046553436365433244435090867457286274743288271182328020372539943012626226269251106032488147015251787776}{463261636424876129938368329678177489488710534372668564138134650863022623301645808169269002974033355712890625} to get \frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{741218618279801807901389327485083983181936854996269702621015441380836197282633293070830404758453369140625}.

$$\frac{\frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{741218618279801807901389327485083983181936854996269702621015441380836197282633293070830404758453369140625}\times \frac{0.08}{14}}{\left(1+\frac{0.08}{18}\right)^{48}-1}$$

Expand \frac{0.08}{14} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{741218618279801807901389327485083983181936854996269702621015441380836197282633293070830404758453369140625}\times \frac{8}{1400}}{\left(1+\frac{0.08}{18}\right)^{48}-1}$$

Reduce the fraction \frac{8}{1400} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{741218618279801807901389327485083983181936854996269702621015441380836197282633293070830404758453369140625}\times \frac{1}{175}}{\left(1+\frac{0.08}{18}\right)^{48}-1}$$

Multiply \frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{741218618279801807901389327485083983181936854996269702621015441380836197282633293070830404758453369140625} and \frac{1}{175} to get \frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375}.

$$\frac{\frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375}}{\left(1+\frac{0.08}{18}\right)^{48}-1}$$

Expand \frac{0.08}{18} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375}}{\left(1+\frac{8}{1800}\right)^{48}-1}$$

Reduce the fraction \frac{8}{1800} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375}}{\left(1+\frac{1}{225}\right)^{48}-1}$$

Add 1 and \frac{1}{225} to get \frac{226}{225}.

$$\frac{\frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375}}{\left(\frac{226}{225}\right)^{48}-1}$$

Calculate \frac{226}{225} to the power of 48 and get \frac{99358512049980541209483346218916889011860073520469901645214345189948485538248014687386249770446260522913340850176}{80308380747696837016746608902131688100817361112568842158825040963704964581959533376220861100591719150543212890625}.

$$\frac{\frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375}}{\frac{99358512049980541209483346218916889011860073520469901645214345189948485538248014687386249770446260522913340850176}{80308380747696837016746608902131688100817361112568842158825040963704964581959533376220861100591719150543212890625}-1}$$

Subtract 1 from \frac{99358512049980541209483346218916889011860073520469901645214345189948485538248014687386249770446260522913340850176}{80308380747696837016746608902131688100817361112568842158825040963704964581959533376220861100591719150543212890625} to get \frac{19050131302283704192736737316785200911042712407901059486389304226243520956288481311165388669854541372370127959551}{80308380747696837016746608902131688100817361112568842158825040963704964581959533376220861100591719150543212890625}.

$$\frac{\frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375}}{\frac{19050131302283704192736737316785200911042712407901059486389304226243520956288481311165388669854541372370127959551}{80308380747696837016746608902131688100817361112568842158825040963704964581959533376220861100591719150543212890625}}$$

Divide \frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375} by \frac{19050131302283704192736737316785200911042712407901059486389304226243520956288481311165388669854541372370127959551}{80308380747696837016746608902131688100817361112568842158825040963704964581959533376220861100591719150543212890625} by multiplying \frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375} by the reciprocal of \frac{19050131302283704192736737316785200911042712407901059486389304226243520956288481311165388669854541372370127959551}{80308380747696837016746608902131688100817361112568842158825040963704964581959533376220861100591719150543212890625}.

$$\frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375}\times \frac{80308380747696837016746608902131688100817361112568842158825040963704964581959533376220861100591719150543212890625}{19050131302283704192736737316785200911042712407901059486389304226243520956288481311165388669854541372370127959551}$$

Multiply \frac{9743792744854981846931910961453879316580395892612338917248325960639088202019620308017696519810352244028604416}{129713258198965316382743132309889697056838949624347197958677702241646334524460826287395320832729339599609375} and \frac{80308380747696837016746608902131688100817361112568842158825040963704964581959533376220861100591719150543212890625}{19050131302283704192736737316785200911042712407901059486389304226243520956288481311165388669854541372370127959551} to get \frac{140901564179851851863678345555776063622360233034359589059751760115268560651490417703026382076781364405058262704899294483332785104463193094405450277217894400}{444947989675330690346955090100013325888077772427841053017859521093097785741166825541953462250920662004615016497029487867414699200211612620929191714392587}.

$$\frac{140901564179851851863678345555776063622360233034359589059751760115268560651490417703026382076781364405058262704899294483332785104463193094405450277217894400}{444947989675330690346955090100013325888077772427841053017859521093097785741166825541953462250920662004615016497029487867414699200211612620929191714392587}$$