Solve 2000{left(1+.075/2right)}^2*6

$$2000 { \left(1+ \frac{ .075 }{ 2 } \right) }^{ 2 \cdot 6 }$$

Evaluate

$$3110.90866274494690617316518910229206085205078125$$

Solution Steps

Expand \frac{0.075}{2} by multiplying both numerator and the denominator by 1000.

$$2000\left(1+\frac{75}{2000}\right)^{2\times 6}$$

Reduce the fraction \frac{75}{2000} to lowest terms by extracting and canceling out 25.

$$2000\left(1+\frac{3}{80}\right)^{2\times 6}$$

Add 1 and \frac{3}{80} to get \frac{83}{80}.

$$2000\times \left(\frac{83}{80}\right)^{2\times 6}$$

Multiply 2 and 6 to get 12.

$$2000\times \left(\frac{83}{80}\right)^{12}$$

Calculate \frac{83}{80} to the power of 12 and get \frac{106890007738661124410161}{68719476736000000000000}.

$$2000\times \frac{106890007738661124410161}{68719476736000000000000}$$

Multiply 2000 and \frac{106890007738661124410161}{68719476736000000000000} to get \frac{106890007738661124410161}{34359738368000000000}.

$$\frac{106890007738661124410161}{34359738368000000000}$$

Factor

$$\frac{83 ^ {12}}{2 ^ {44} \cdot 5 ^ {9}} = 3110\frac{3.1221414181119984 \times 10^{19}}{3.4359738368 \times 10^{19}} = 3110.908662744947$$