Solve 400000*0.05*1.05^20/1.05^20-1

$$\frac { 400000 \times 0.05 \times 1.05 ^ { 20 } } { 1.05 ^ { 20 } - 1 }$$

Evaluate

$$\frac{5564368588939030972743928020000}{173360829446951548637196401}\approx 32097.034876277$$

Solution Steps

Multiply 400000 and 0.05 to get 20000.

$$\frac{20000\times 1.05^{20}}{1.05^{20}-1}$$

Calculate 1.05 to the power of 20 and get 2.6532977051444201339454307651519775390625.

$$\frac{20000\times 2.6532977051444201339454307651519775390625}{1.05^{20}-1}$$

Multiply 20000 and 2.6532977051444201339454307651519775390625 to get 53065.95410288840267890861530303955078125.

$$\frac{53065.95410288840267890861530303955078125}{1.05^{20}-1}$$

Calculate 1.05 to the power of 20 and get 2.6532977051444201339454307651519775390625.

$$\frac{53065.95410288840267890861530303955078125}{2.6532977051444201339454307651519775390625-1}$$

Subtract 1 from 2.6532977051444201339454307651519775390625 to get 1.6532977051444201339454307651519775390625.

$$\frac{53065.95410288840267890861530303955078125}{1.6532977051444201339454307651519775390625}$$

Expand \frac{53065.95410288840267890861530303955078125}{1.6532977051444201339454307651519775390625} by multiplying both numerator and the denominator by 10000000000000000000000000000000000000000.

$$\frac{530659541028884026789086153030395507812500000}{16532977051444201339454307651519775390625}$$

Reduce the fraction \frac{530659541028884026789086153030395507812500000}{16532977051444201339454307651519775390625} to lowest terms by extracting and canceling out 95367431640625.

$$\frac{5564368588939030972743928020000}{173360829446951548637196401}$$

Factor

$$\frac{2 ^ {5} \cdot 3 ^ {20} \cdot 5 ^ {4} \cdot 7 ^ {20}}{11 \cdot 31 \cdot 41 \cdot 331 \cdot 521 \cdot 1601 \cdot 2671 \cdot 19993361 \cdot 29 ^ {2}} = 32097\frac{6.04618022745916 \times 10^{24}}{1.7336082944695153 \times 10^{26}} = 32097.03487627653$$