Finite Math Examples

$240000 = \frac{p ({(1 + \frac{0.035}{12})}^{36} - 1)}{\frac{0.035}{12}}$

Step 1

Rewrite the equation as $\frac{p ({(1 + \frac{0.035}{12})}^{36} - 1)}{\frac{0.035}{12}} = 240000$ .

$\frac{p ({(1 + \frac{0.035}{12})}^{36} - 1)}{\frac{0.035}{12}} = 240000$

Step 2

Multiply both sides of the equation by $\frac{\frac{0.035}{12}}{{(1 + \frac{0.035}{12})}^{36} - 1}$ .

$\frac{\frac{0.035}{12}}{{(1 + \frac{0.035}{12})}^{36} - 1} \cdot \frac{p ({(1 + \frac{0.035}{12})}^{36} - 1)}{\frac{0.035}{12}} = \frac{\frac{0.035}{12}}{{(1 + \frac{0.035}{12})}^{36} - 1} \cdot 240000$

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 $\frac{\frac{0.035}{12}}{{(1 + \frac{0.035}{12})}^{36} - 1} \cdot \frac{p ({(1 + \frac{0.035}{12})}^{36} - 1)}{\frac{0.035}{12}}$ .

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Step 3.1.1.1

Cancel the common factor of $\frac{0.035}{12}$ .

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Step 3.1.1.1.1

Cancel the common factor.

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{{(1 + \frac{0.035}{12})}^{36} - 1} (p ({(1 + \frac{0.035}{12})}^{36} - 1)) = \frac{\frac{0.035}{12}}{{(1 + \frac{0.035}{12})}^{36} - 1} \cdot 240000$

Step 3.1.1.2

Cancel the common factor of ${(1 + \frac{0.035}{12})}^{36} - 1$ .

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Step 3.1.1.2.1

Factor ${(1 + \frac{0.035}{12})}^{36} - 1$ out of $p ({(1 + \frac{0.035}{12})}^{36} - 1)$ .

$\frac{1}{{(1 + \frac{0.035}{12})}^{36} - 1} (({(1 + \frac{0.035}{12})}^{36} - 1) p) = \frac{\frac{0.035}{12}}{{(1 + \frac{0.035}{12})}^{36} - 1} \cdot 240000$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{{(1 + \frac{0.035}{12})}^{36} - 1} (({(1 + \frac{0.035}{12})}^{36} - 1) p) = \frac{\frac{0.035}{12}}{{(1 + \frac{0.035}{12})}^{36} - 1} \cdot 240000$

Step 3.1.1.2.3

Rewrite the expression.

$p = \frac{\frac{0.035}{12}}{{(1 + \frac{0.035}{12})}^{36} - 1} \cdot 240000$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{\frac{0.035}{12}}{{(1 + \frac{0.035}{12})}^{36} - 1} \cdot 240000$ .

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Step 3.2.1.1

Divide $0.035$ by $12$ .

$p = \frac{0.00291\overline{6}}{{(1 + \frac{0.035}{12})}^{36} - 1} \cdot 240000$

Step 3.2.1.2

Simplify the denominator.

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Step 3.2.1.2.1

Divide $0.035$ by $12$ .

$p = \frac{0.00291\overline{6}}{{(1 + 0.00291\overline{6})}^{36} - 1} \cdot 240000$

Step 3.2.1.2.2

Add $1$ and $0.00291\overline{6}$ .

$p = \frac{0.00291\overline{6}}{{1.00291\overline{6}}^{36} - 1} \cdot 240000$

Step 3.2.1.2.3

Raise $1.00291\overline{6}$ to the power of $36$ .

$p = \frac{0.00291\overline{6}}{1.11054087 - 1} \cdot 240000$

Step 3.2.1.2.4

Subtract $1$ from $1.11054087$ .

$p = \frac{0.00291\overline{6}}{0.11054087} \cdot 240000$

Step 3.2.1.3

Simplify the expression.

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Step 3.2.1.3.1

Divide $0.00291\overline{6}$ by $0.11054087$ .

$p = 0.02638541 \cdot 240000$

Step 3.2.1.3.2

Multiply $0.02638541$ by $240000$ .

$p = 6332.49913445$