Solve 20000*1.1^8-1/0.1*(1+0.1)^8

$$20000 \times \frac { 1.1 ^ { 8 } - 1 } { 0.1 \times ( 1 + 0.1 ) ^ { 8 } }$$

Evaluate

$$\frac{22871776200000}{214358881}\approx 106698.523958053$$

Solution Steps

Calculate 1.1 to the power of 8 and get 2.14358881.

$$20000\times \frac{2.14358881-1}{0.1\left(1+0.1\right)^{8}}$$

Subtract 1 from 2.14358881 to get 1.14358881.

$$20000\times \frac{1.14358881}{0.1\left(1+0.1\right)^{8}}$$

Add 1 and 0.1 to get 1.1.

$$20000\times \frac{1.14358881}{0.1\times 1.1^{8}}$$

Calculate 1.1 to the power of 8 and get 2.14358881.

$$20000\times \frac{1.14358881}{0.1\times 2.14358881}$$

Multiply 0.1 and 2.14358881 to get 0.214358881.

$$20000\times \frac{1.14358881}{0.214358881}$$

Expand \frac{1.14358881}{0.214358881} by multiplying both numerator and the denominator by 1000000000.

$$20000\times \frac{1143588810}{214358881}$$

Multiply 20000 and \frac{1143588810}{214358881} to get \frac{22871776200000}{214358881}.

$$\frac{22871776200000}{214358881}$$

Factor

$$\frac{3 \cdot 7 \cdot 13 \cdot 17 \cdot 41 \cdot 601 \cdot 2 ^ {6} \cdot 5 ^ {5}}{11 ^ {8}} = 106698\frac{112315062}{214358881} = 106698.52395805332$$