Finite Math Examples

$6000 = \frac{p (1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3})}{\frac{0.144}{12}}$

Step 1

Rewrite the equation as $\frac{p (1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3})}{\frac{0.144}{12}} = 6000$ .

$\frac{p (1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3})}{\frac{0.144}{12}} = 6000$

Step 2

Multiply both sides of the equation by $\frac{\frac{0.144}{12}}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}}$ .

$\frac{\frac{0.144}{12}}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} \cdot \frac{p (1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3})}{\frac{0.144}{12}} = \frac{\frac{0.144}{12}}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} \cdot 6000$

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 $\frac{\frac{0.144}{12}}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} \cdot \frac{p (1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3})}{\frac{0.144}{12}}$ .

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Step 3.1.1.1

Cancel the common factor of $\frac{0.144}{12}$ .

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Step 3.1.1.1.1

Cancel the common factor.

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} (p (1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3})) = \frac{\frac{0.144}{12}}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} \cdot 6000$

Step 3.1.1.2

Cancel the common factor of $1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}$ .

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Step 3.1.1.2.1

Factor $1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}$ out of $p (1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3})$ .

$\frac{1}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} ((1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}) p) = \frac{\frac{0.144}{12}}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} \cdot 6000$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} ((1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}) p) = \frac{\frac{0.144}{12}}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} \cdot 6000$

Step 3.1.1.2.3

Rewrite the expression.

$p = \frac{\frac{0.144}{12}}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} \cdot 6000$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{\frac{0.144}{12}}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} \cdot 6000$ .

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Step 3.2.1.1

Divide $0.144$ by $12$ .

$p = \frac{0.012}{1 - {(1 + \frac{0.144}{12})}^{- 12 \cdot 3}} \cdot 6000$

Step 3.2.1.2

Simplify the denominator.

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Step 3.2.1.2.1

Divide $0.144$ by $12$ .

$p = \frac{0.012}{1 - {(1 + 0.012)}^{- 12 \cdot 3}} \cdot 6000$

Step 3.2.1.2.2

Add $1$ and $0.012$ .

$p = \frac{0.012}{1 - {1.012}^{- 12 \cdot 3}} \cdot 6000$

Step 3.2.1.2.3

Multiply $- 12$ by $3$ .

$p = \frac{0.012}{1 - {1.012}^{- 36}} \cdot 6000$

Step 3.2.1.2.4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$p = \frac{0.012}{1 - \frac{1}{{1.012}^{36}}} \cdot 6000$

Step 3.2.1.2.5

Raise $1.012$ to the power of $36$ .

$p = \frac{0.012}{1 - \frac{1}{1.53637931}} \cdot 6000$

Step 3.2.1.2.6

Divide $1$ by $1.53637931$ .

$p = \frac{0.012}{1 - 1 \cdot 0.65088093} \cdot 6000$

Step 3.2.1.2.7

Multiply $- 1$ by $0.65088093$ .

$p = \frac{0.012}{1 - 0.65088093} \cdot 6000$

Step 3.2.1.2.8

Subtract $0.65088093$ from $1$ .

$p = \frac{0.012}{0.34911906} \cdot 6000$

Step 3.2.1.3

Simplify the expression.

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Step 3.2.1.3.1

Divide $0.012$ by $0.34911906$ .

$p = 0.03437222 \cdot 6000$

Step 3.2.1.3.2

Multiply $0.03437222$ by $6000$ .

$p = 206.23336544$