Solve 2500{left(1+0.05/2right)}^2*1frac{1{2}}

$$2500 { \left( 1+ \frac{ 0.05 }{ 2 } \right) }^{ 2 \times 1 \frac{ 1 }{ 2 } }$$

Evaluate

$$2692.2265625$$

Solution Steps

Expand \frac{0.05}{2} by multiplying both numerator and the denominator by 100.

$$2500\left(1+\frac{5}{200}\right)^{2\times \frac{1\times 2+1}{2}}$$

Reduce the fraction \frac{5}{200} to lowest terms by extracting and canceling out 5.

$$2500\left(1+\frac{1}{40}\right)^{2\times \frac{1\times 2+1}{2}}$$

Add 1 and \frac{1}{40} to get \frac{41}{40}.

$$2500\times \left(\frac{41}{40}\right)^{2\times \frac{1\times 2+1}{2}}$$

Multiply 1 and 2 to get 2.

$$2500\times \left(\frac{41}{40}\right)^{2\times \frac{2+1}{2}}$$

Add 2 and 1 to get 3.

$$2500\times \left(\frac{41}{40}\right)^{2\times \frac{3}{2}}$$

Multiply 2 and \frac{3}{2} to get 3.

$$2500\times \left(\frac{41}{40}\right)^{3}$$

Calculate \frac{41}{40} to the power of 3 and get \frac{68921}{64000}.

$$2500\times \frac{68921}{64000}$$

Multiply 2500 and \frac{68921}{64000} to get \frac{344605}{128}.

$$\frac{344605}{128}$$

Factor

$$\frac{5 \cdot 41 ^ {3}}{2 ^ {7}} = 2692\frac{29}{128} = 2692.2265625$$