Precalculus Examples

$A = 50 {(1 + \frac{r}{12})}^{12}$

Step 1

Rewrite the equation as $50 {(1 + \frac{r}{12})}^{12} = A$ .

$50 {(1 + \frac{r}{12})}^{12} = A$

Step 2

Divide each term in $50 {(1 + \frac{r}{12})}^{12} = A$ by $50$ and simplify.

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Step 2.1

Divide each term in $50 {(1 + \frac{r}{12})}^{12} = A$ by $50$ .

$\frac{50 {(1 + \frac{r}{12})}^{12}}{50} = \frac{A}{50}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $50$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{50 {(1 + \frac{r}{12})}^{12}}{50} = \frac{A}{50}$

Step 2.2.1.2

Divide ${(1 + \frac{r}{12})}^{12}$ by $1$ .

${(1 + \frac{r}{12})}^{12} = \frac{A}{50}$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$1 + \frac{r}{12} = \pm \sqrt[12]{\frac{A}{50}}$

Step 4

Rewrite $\sqrt[12]{\frac{A}{50}}$ as $\frac{\sqrt[12]{A}}{\sqrt[12]{50}}$ .

$1 + \frac{r}{12} = \pm \frac{\sqrt[12]{A}}{\sqrt[12]{50}}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$1 + \frac{r}{12} = \frac{\sqrt[12]{A}}{\sqrt[12]{50}}$

Step 5.2

Subtract $1$ from both sides of the equation.

$\frac{r}{12} = \frac{\sqrt[12]{A}}{\sqrt[12]{50}} - 1$

Step 5.3

Multiply both sides of the equation by $12$ .

$12 \frac{r}{12} = 12 (\frac{\sqrt[12]{A}}{\sqrt[12]{50}} - 1)$

Step 5.4

Simplify both sides of the equation.

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Step 5.4.1

Simplify the left side.

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Step 5.4.1.1

Cancel the common factor of $12$ .

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Step 5.4.1.1.1

Cancel the common factor.

$12 \frac{r}{12} = 12 (\frac{\sqrt[12]{A}}{\sqrt[12]{50}} - 1)$

Step 5.4.1.1.2

Rewrite the expression.

$r = 12 (\frac{\sqrt[12]{A}}{\sqrt[12]{50}} - 1)$

Step 5.4.2

Simplify the right side.

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Step 5.4.2.1

Simplify $12 (\frac{\sqrt[12]{A}}{\sqrt[12]{50}} - 1)$ .

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Step 5.4.2.1.1

Apply the distributive property.

$r = 12 \frac{\sqrt[12]{A}}{\sqrt[12]{50}} + 12 \cdot - 1$

Step 5.4.2.1.2

Combine $12$ and $\frac{\sqrt[12]{A}}{\sqrt[12]{50}}$ .

$r = \frac{12 \sqrt[12]{A}}{\sqrt[12]{50}} + 12 \cdot - 1$

Step 5.4.2.1.3

Multiply $12$ by $- 1$ .

$r = \frac{12 \sqrt[12]{A}}{\sqrt[12]{50}} - 12$

Step 5.5

Next, use the negative value of the $\pm$ to find the second solution.

$1 + \frac{r}{12} = - \frac{\sqrt[12]{A}}{\sqrt[12]{50}}$

Step 5.6

Subtract $1$ from both sides of the equation.

$\frac{r}{12} = - \frac{\sqrt[12]{A}}{\sqrt[12]{50}} - 1$

Step 5.7

Multiply both sides of the equation by $12$ .

$12 \frac{r}{12} = 12 (- \frac{\sqrt[12]{A}}{\sqrt[12]{50}} - 1)$

Step 5.8

Simplify both sides of the equation.

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Step 5.8.1

Simplify the left side.

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Step 5.8.1.1

Cancel the common factor of $12$ .

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Step 5.8.1.1.1

Cancel the common factor.

$12 \frac{r}{12} = 12 (- \frac{\sqrt[12]{A}}{\sqrt[12]{50}} - 1)$

Step 5.8.1.1.2

Rewrite the expression.

$r = 12 (- \frac{\sqrt[12]{A}}{\sqrt[12]{50}} - 1)$

Step 5.8.2

Simplify the right side.

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Step 5.8.2.1

Simplify $12 (- \frac{\sqrt[12]{A}}{\sqrt[12]{50}} - 1)$ .

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Step 5.8.2.1.1

Apply the distributive property.

$r = 12 (- \frac{\sqrt[12]{A}}{\sqrt[12]{50}}) + 12 \cdot - 1$

Step 5.8.2.1.2

Multiply $12 (- \frac{\sqrt[12]{A}}{\sqrt[12]{50}})$ .

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Step 5.8.2.1.2.1

Multiply $- 1$ by $12$ .

$r = - 12 \frac{\sqrt[12]{A}}{\sqrt[12]{50}} + 12 \cdot - 1$

Step 5.8.2.1.2.2

Combine $- 12$ and $\frac{\sqrt[12]{A}}{\sqrt[12]{50}}$ .

$r = \frac{- 12 \sqrt[12]{A}}{\sqrt[12]{50}} + 12 \cdot - 1$

Step 5.8.2.1.3

Multiply $12$ by $- 1$ .

$r = \frac{- 12 \sqrt[12]{A}}{\sqrt[12]{50}} - 12$

Step 5.8.2.1.4

Move the negative in front of the fraction.

$r = - \frac{12 \sqrt[12]{A}}{\sqrt[12]{50}} - 12$

Step 5.9

The complete solution is the result of both the positive and negative portions of the solution.

$r = \frac{12 \sqrt[12]{A}}{\sqrt[12]{50}} - 12$

$r = - \frac{12 \sqrt[12]{A}}{\sqrt[12]{50}} - 12$

$r = \frac{12 \sqrt[12]{A}}{\sqrt[12]{50}} - 12$

$r = - \frac{12 \sqrt[12]{A}}{\sqrt[12]{50}} - 12$