Solve ({left(frac{1+0.13/1+.1255right)}^5-1}{0.13-0.125})

$$( \frac{ { \left( \frac{ 1+0.13 }{ 1+.1255 } \right) }^{ 5 } -1 }{ 0.13-0.125 } )$$

Evaluate

$$\frac{232925637392749800}{57793297550636251}\approx 4.030322672$$

Solution Steps

Add 1 and 0.13 to get 1.13.

$$\frac{\left(\frac{1.13}{1+0.1255}\right)^{5}-1}{0.13-0.125}$$

Add 1 and 0.1255 to get 1.1255.

$$\frac{\left(\frac{1.13}{1.1255}\right)^{5}-1}{0.13-0.125}$$

Expand \frac{1.13}{1.1255} by multiplying both numerator and the denominator by 10000.

$$\frac{\left(\frac{11300}{11255}\right)^{5}-1}{0.13-0.125}$$

Reduce the fraction \frac{11300}{11255} to lowest terms by extracting and canceling out 5.

$$\frac{\left(\frac{2260}{2251}\right)^{5}-1}{0.13-0.125}$$

Calculate \frac{2260}{2251} to the power of 5 and get \frac{58957925737600000}{57793297550636251}.

$$\frac{\frac{58957925737600000}{57793297550636251}-1}{0.13-0.125}$$

Subtract 1 from \frac{58957925737600000}{57793297550636251} to get \frac{1164628186963749}{57793297550636251}.

$$\frac{\frac{1164628186963749}{57793297550636251}}{0.13-0.125}$$

Subtract 0.125 from 0.13 to get 0.005.

$$\frac{\frac{1164628186963749}{57793297550636251}}{0.005}$$

Express \frac{\frac{1164628186963749}{57793297550636251}}{0.005} as a single fraction.

$$\frac{1164628186963749}{57793297550636251\times 0.005}$$

Multiply 57793297550636251 and 0.005 to get 288966487753181.255.

$$\frac{1164628186963749}{288966487753181.255}$$

Expand \frac{1164628186963749}{288966487753181.255} by multiplying both numerator and the denominator by 1000.

$$\frac{1164628186963749000}{288966487753181255}$$

Reduce the fraction \frac{1164628186963749000}{288966487753181255} to lowest terms by extracting and canceling out 5.

$$\frac{232925637392749800}{57793297550636251}$$

Factor

$$\frac{31 \cdot 4174294576931 \cdot 2 ^ {3} \cdot 3 ^ {2} \cdot 5 ^ {2}}{2251 ^ {5}} = 4\frac{1752447190204800}{57793297550636250} = 4.030322671736621$$