Solve 5000(1+1.4/100.12)^5+12

$$5000 ( 1 + \frac { 1.4 } { 100.12 } ) ^ { 5 + 12 }$$

Evaluate

$$\frac{37612093429163781022523776244369765655734065989489255383040000}{5940656526890832165304677930351212720236719525275564782663}\approx 6331.302484651$$

Solution Steps

Expand \frac{1.4}{100.12} by multiplying both numerator and the denominator by 100.

$$5000\left(1+\frac{140}{10012}\right)^{5+12}$$

Reduce the fraction \frac{140}{10012} to lowest terms by extracting and canceling out 4.

$$5000\left(1+\frac{35}{2503}\right)^{5+12}$$

Add 1 and \frac{35}{2503} to get \frac{2538}{2503}.

$$5000\times \left(\frac{2538}{2503}\right)^{5+12}$$

Add 5 and 12 to get 17.

$$5000\times \left(\frac{2538}{2503}\right)^{17}$$

Calculate \frac{2538}{2503} to the power of 17 and get \frac{7522418685832756204504755248873953131146813197897851076608}{5940656526890832165304677930351212720236719525275564782663}.

$$5000\times \frac{7522418685832756204504755248873953131146813197897851076608}{5940656526890832165304677930351212720236719525275564782663}$$

Multiply 5000 and \frac{7522418685832756204504755248873953131146813197897851076608}{5940656526890832165304677930351212720236719525275564782663} to get \frac{37612093429163781022523776244369765655734065989489255383040000}{5940656526890832165304677930351212720236719525275564782663}.

$$\frac{37612093429163781022523776244369765655734065989489255383040000}{5940656526890832165304677930351212720236719525275564782663}$$

Factor

$$\frac{2 ^ {20} \cdot 3 ^ {51} \cdot 5 ^ {4} \cdot 47 ^ {17}}{2503 ^ {17}} = 6331\frac{1.7969574179256993 \times 10^{57}}{5.940656526890832 \times 10^{57}} = 6331.302484651283$$