Finite Math Examples

$12000 = r (\frac{{(1 + \frac{0.022}{4})}^{4.5} - 1}{\frac{0.022}{4}})$

Step 1

Rewrite the equation as $r (\frac{{(1 + \frac{0.022}{4})}^{4.5} - 1}{\frac{0.022}{4}}) = 12000$ .

$r (\frac{{(1 + \frac{0.022}{4})}^{4.5} - 1}{\frac{0.022}{4}}) = 12000$

Step 2

Simplify.

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Step 2.1

Divide $0.022$ by $4$ .

$r \frac{{(1 + 0.0055)}^{4.5} - 1}{\frac{0.022}{4}} = 12000$

Step 2.2

Divide $0.022$ by $4$ .

$r \frac{{(1 + 0.0055)}^{4.5} - 1}{0.0055} = 12000$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Add $1$ and $0.0055$ .

$r \frac{{1.0055}^{4.5} - 1}{0.0055} = 12000$

Step 2.3.2

Raise $1.0055$ to the power of $4.5$ .

$r \frac{1.02498931 - 1}{0.0055} = 12000$

Step 2.3.3

Subtract $1$ from $1.02498931$ .

$r \frac{0.02498931}{0.0055} = 12000$

Step 2.4

Divide $0.02498931$ by $0.0055$ .

$r \cdot 4.54351142 = 12000$

Step 3

Divide each term in $r \cdot 4.54351142 = 12000$ by $4.54351142$ and simplify.

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Step 3.1

Divide each term in $r \cdot 4.54351142 = 12000$ by $4.54351142$ .

$\frac{r \cdot 4.54351142}{4.54351142} = \frac{12000}{4.54351142}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4.54351142$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{r \cdot 4.54351142}{4.54351142} = \frac{12000}{4.54351142}$

Step 3.2.1.2

Divide $r$ by $1$ .

$r = \frac{12000}{4.54351142}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $12000$ by $4.54351142$ .

$r = 2641.12904684$