Solve 12,000(0.05/12)/1-(1+frac{0.05{12})^(-12)(5)}

$$\frac { 12,000 ( \frac { 0.05 } { 12 } ) } { 1 - ( 1 + \frac { 0.05 } { 12 } ) ^ { ( - 12 ) ( 5 ) } }$$

Evaluate

$$\frac{4168622409200893119184666279937280310472481032640802402127015397362477944597141659701356445832798717894786760074605163805693729317272098282320050}{18408187155108906318889826761915234524703579296438862514551969280291864329552587818027128916655974357895735201492103276113874586345441965646401}\approx 226.454803728$$

Solution Steps

Expand \frac{0.05}{12} by multiplying both numerator and the denominator by 100.

$$\frac{12000\times \frac{5}{1200}}{1-\left(1+\frac{0.05}{12}\right)^{-12\times 5}}$$

Reduce the fraction \frac{5}{1200} to lowest terms by extracting and canceling out 5.

$$\frac{12000\times \frac{1}{240}}{1-\left(1+\frac{0.05}{12}\right)^{-12\times 5}}$$

Multiply 12000 and \frac{1}{240} to get 50.

$$\frac{50}{1-\left(1+\frac{0.05}{12}\right)^{-12\times 5}}$$

Expand \frac{0.05}{12} by multiplying both numerator and the denominator by 100.

$$\frac{50}{1-\left(1+\frac{5}{1200}\right)^{-12\times 5}}$$

Reduce the fraction \frac{5}{1200} to lowest terms by extracting and canceling out 5.

$$\frac{50}{1-\left(1+\frac{1}{240}\right)^{-12\times 5}}$$

Add 1 and \frac{1}{240} to get \frac{241}{240}.

$$\frac{50}{1-\left(\frac{241}{240}\right)^{-12\times 5}}$$

Multiply -12 and 5 to get -60.

$$\frac{50}{1-\left(\frac{241}{240}\right)^{-60}}$$

Calculate \frac{241}{240} to the power of -60 and get \frac{64964261028908956064803498836830371684746041356377185527988338666957694562390245376000000000000000000000000000000000000000000000000000000000000}{83372448184017862383693325598745606209449620652816048042540307947249558891942833194027128916655974357895735201492103276113874586345441965646401}.

$$\frac{50}{1-\frac{64964261028908956064803498836830371684746041356377185527988338666957694562390245376000000000000000000000000000000000000000000000000000000000000}{83372448184017862383693325598745606209449620652816048042540307947249558891942833194027128916655974357895735201492103276113874586345441965646401}}$$

Subtract \frac{64964261028908956064803498836830371684746041356377185527988338666957694562390245376000000000000000000000000000000000000000000000000000000000000}{83372448184017862383693325598745606209449620652816048042540307947249558891942833194027128916655974357895735201492103276113874586345441965646401} from 1 to get \frac{18408187155108906318889826761915234524703579296438862514551969280291864329552587818027128916655974357895735201492103276113874586345441965646401}{83372448184017862383693325598745606209449620652816048042540307947249558891942833194027128916655974357895735201492103276113874586345441965646401}.

$$\frac{50}{\frac{18408187155108906318889826761915234524703579296438862514551969280291864329552587818027128916655974357895735201492103276113874586345441965646401}{83372448184017862383693325598745606209449620652816048042540307947249558891942833194027128916655974357895735201492103276113874586345441965646401}}$$

Divide 50 by \frac{18408187155108906318889826761915234524703579296438862514551969280291864329552587818027128916655974357895735201492103276113874586345441965646401}{83372448184017862383693325598745606209449620652816048042540307947249558891942833194027128916655974357895735201492103276113874586345441965646401} by multiplying 50 by the reciprocal of \frac{18408187155108906318889826761915234524703579296438862514551969280291864329552587818027128916655974357895735201492103276113874586345441965646401}{83372448184017862383693325598745606209449620652816048042540307947249558891942833194027128916655974357895735201492103276113874586345441965646401}.

$$50\times \frac{83372448184017862383693325598745606209449620652816048042540307947249558891942833194027128916655974357895735201492103276113874586345441965646401}{18408187155108906318889826761915234524703579296438862514551969280291864329552587818027128916655974357895735201492103276113874586345441965646401}$$

Multiply 50 and \frac{83372448184017862383693325598745606209449620652816048042540307947249558891942833194027128916655974357895735201492103276113874586345441965646401}{18408187155108906318889826761915234524703579296438862514551969280291864329552587818027128916655974357895735201492103276113874586345441965646401} to get \frac{4168622409200893119184666279937280310472481032640802402127015397362477944597141659701356445832798717894786760074605163805693729317272098282320050}{18408187155108906318889826761915234524703579296438862514551969280291864329552587818027128916655974357895735201492103276113874586345441965646401}.

$$\frac{4168622409200893119184666279937280310472481032640802402127015397362477944597141659701356445832798717894786760074605163805693729317272098282320050}{18408187155108906318889826761915234524703579296438862514551969280291864329552587818027128916655974357895735201492103276113874586345441965646401}$$