Solve {left(1+.05/2.05right)}^12

$${ \left(1+ \frac{ .05 }{ 2.05 } \right) }^{ 12 }$$

Evaluate

$$\frac{30129469486639681536}{22563490300366186081}\approx 1.33531954$$

Solution Steps

Expand \frac{0.05}{2.05} by multiplying both numerator and the denominator by 100.

$$\left(1+\frac{5}{205}\right)^{12}$$

Reduce the fraction \frac{5}{205} to lowest terms by extracting and canceling out 5.

$$\left(1+\frac{1}{41}\right)^{12}$$

Add 1 and \frac{1}{41} to get \frac{42}{41}.

$$\left(\frac{42}{41}\right)^{12}$$

Calculate \frac{42}{41} to the power of 12 and get \frac{30129469486639681536}{22563490300366186081}.

$$\frac{30129469486639681536}{22563490300366186081}$$

Factor

$$\frac{2 ^ {12} \cdot 3 ^ {12} \cdot 7 ^ {12}}{41 ^ {12}} = 1\frac{7.5659791862734975 \times 10^{18}}{2.2563490300366182 \times 10^{19}} = 1.3353195399095994$$