Finite Math Examples

$81000 = \frac{x ({(1 + 0.005)}^{228} - 1)}{0.005}$

Step 1

Rewrite the equation as $\frac{x ({(1 + 0.005)}^{228} - 1)}{0.005} = 81000$ .

$\frac{x ({(1 + 0.005)}^{228} - 1)}{0.005} = 81000$

Step 2

Multiply both sides of the equation by $\frac{0.005}{{(1 + 0.005)}^{228} - 1}$ .

$\frac{0.005}{{(1 + 0.005)}^{228} - 1} \cdot \frac{x ({(1 + 0.005)}^{228} - 1)}{0.005} = \frac{0.005}{{(1 + 0.005)}^{228} - 1} \cdot 81000$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{0.005}{{(1 + 0.005)}^{228} - 1} \cdot \frac{x ({(1 + 0.005)}^{228} - 1)}{0.005}$ .

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Step 3.1.1.1

Cancel the common factor of $0.005$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{0.005}{{(1 + 0.005)}^{228} - 1} \cdot \frac{x ({(1 + 0.005)}^{228} - 1)}{0.005} = \frac{0.005}{{(1 + 0.005)}^{228} - 1} \cdot 81000$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{{(1 + 0.005)}^{228} - 1} (x ({(1 + 0.005)}^{228} - 1)) = \frac{0.005}{{(1 + 0.005)}^{228} - 1} \cdot 81000$

Step 3.1.1.2

Cancel the common factor of ${(1 + 0.005)}^{228} - 1$ .

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Step 3.1.1.2.1

Factor ${(1 + 0.005)}^{228} - 1$ out of $x ({(1 + 0.005)}^{228} - 1)$ .

$\frac{1}{{(1 + 0.005)}^{228} - 1} (({(1 + 0.005)}^{228} - 1) x) = \frac{0.005}{{(1 + 0.005)}^{228} - 1} \cdot 81000$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{{(1 + 0.005)}^{228} - 1} (({(1 + 0.005)}^{228} - 1) x) = \frac{0.005}{{(1 + 0.005)}^{228} - 1} \cdot 81000$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{0.005}{{(1 + 0.005)}^{228} - 1} \cdot 81000$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{0.005}{{(1 + 0.005)}^{228} - 1} \cdot 81000$ .

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Step 3.2.1.1

Simplify the denominator.

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Step 3.2.1.1.1

Add $1$ and $0.005$ .

$x = \frac{0.005}{{1.005}^{228} - 1} \cdot 81000$

Step 3.2.1.1.2

Raise $1.005$ to the power of $228$ .

$x = \frac{0.005}{3.11789927 - 1} \cdot 81000$

Step 3.2.1.1.3

Subtract $1$ from $3.11789927$ .

$x = \frac{0.005}{2.11789927} \cdot 81000$

Step 3.2.1.2

Simplify terms.

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Step 3.2.1.2.1

Cancel the common factor of $0.005$ .

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Step 3.2.1.2.1.1

Cancel the common factor.

$x = \frac{0.005}{2.11789927} \cdot 81000$

Step 3.2.1.2.1.2

Rewrite the expression.

$x = \frac{1}{2.11789927} \cdot \frac{81000}{200}$

Step 3.2.1.2.2

Multiply $\frac{1}{2.11789927}$ by $\frac{81000}{200}$ .

$x = \frac{81000}{2.11789927 \cdot 200}$

Step 3.2.1.2.3

Simplify the expression.

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Step 3.2.1.2.3.1

Multiply $2.11789927$ by $200$ .

$x = \frac{81000}{423.57985422}$

Step 3.2.1.2.3.2

Divide $81000$ by $423.57985422$ .

$x = 191.22722478$