Solve 300000/0.10-0.20[1-(1+0.20/1+0.10)^5]

$$\frac { 300000 } { 0.10 - 0.20 } [ 1 - ( \frac { 1 + 0.20 } { 1 + 0.10 } ) ^ { 5 } ]$$

Evaluate

$$\frac{263343000000}{161051}\approx 1635152.839783671$$

Solution Steps

Subtract 0.2 from 0.1 to get -0.1.

$$\frac{300000}{-0.1}\left(1-\left(\frac{1+0.2}{1+0.1}\right)^{5}\right)$$

Expand \frac{300000}{-0.1} by multiplying both numerator and the denominator by 10.

$$\frac{3000000}{-1}\left(1-\left(\frac{1+0.2}{1+0.1}\right)^{5}\right)$$

Fraction \frac{3000000}{-1} can be rewritten as -3000000 by extracting the negative sign.

$$-3000000\left(1-\left(\frac{1+0.2}{1+0.1}\right)^{5}\right)$$

Add 1 and 0.2 to get 1.2.

$$-3000000\left(1-\left(\frac{1.2}{1+0.1}\right)^{5}\right)$$

Add 1 and 0.1 to get 1.1.

$$-3000000\left(1-\left(\frac{1.2}{1.1}\right)^{5}\right)$$

Expand \frac{1.2}{1.1} by multiplying both numerator and the denominator by 10.

$$-3000000\left(1-\left(\frac{12}{11}\right)^{5}\right)$$

Calculate \frac{12}{11} to the power of 5 and get \frac{248832}{161051}.

$$-3000000\left(1-\frac{248832}{161051}\right)$$

Subtract \frac{248832}{161051} from 1 to get -\frac{87781}{161051}.

$$-3000000\left(-\frac{87781}{161051}\right)$$

Multiply -3000000 and -\frac{87781}{161051} to get \frac{263343000000}{161051}.

$$\frac{263343000000}{161051}$$

Factor

$$\frac{3 \cdot 41 \cdot 2141 \cdot 2 ^ {6} \cdot 5 ^ {6}}{11 ^ {5}} = 1635152\frac{135248}{161051} = 1635152.839783671$$