Solve for r 7000=5000(1+r/12)^120

$7000 = 5000 {(1 + \frac{r}{12})}^{120}$

Rewrite the equation as $5000 {(1 + \frac{r}{12})}^{120} = 7000$ .

$5000 {(1 + \frac{r}{12})}^{120} = 7000$

Divide each term by $5000$ and simplify.

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Divide each term in $5000 {(1 + \frac{r}{12})}^{120} = 7000$ by $5000$ .

$\frac{5000 {(1 + \frac{r}{12})}^{120}}{5000} = \frac{7000}{5000}$

Cancel the common factor of $5000$ .

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Cancel the common factor.

$\frac{5000 {(1 + \frac{r}{12})}^{120}}{5000} = \frac{7000}{5000}$

Divide ${(1 + \frac{r}{12})}^{120}$ by $1$ .

${(1 + \frac{r}{12})}^{120} = \frac{7000}{5000}$

Cancel the common factor of $7000$ and $5000$ .

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Factor $1000$ out of $7000$ .

${(1 + \frac{r}{12})}^{120} = \frac{1000 (7)}{5000}$

Cancel the common factors.

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Factor $1000$ out of $5000$ .

${(1 + \frac{r}{12})}^{120} = \frac{1000 \cdot 7}{1000 \cdot 5}$

Cancel the common factor.

${(1 + \frac{r}{12})}^{120} = \frac{1000 \cdot 7}{1000 \cdot 5}$

Rewrite the expression.

${(1 + \frac{r}{12})}^{120} = \frac{7}{5}$

Take the $120th$ root of each side of the $equation$ to set up the solution for $r$

${(1 + \frac{r}{12})}^{120 \cdot \frac{1}{120}} = \pm \sqrt[120]{\frac{7}{5}}$

Remove the perfect root factor $1 + \frac{r}{12}$ under the radical to solve for $r$ .

$1 + \frac{r}{12} = \pm \sqrt[120]{\frac{7}{5}}$

Rewrite $\sqrt[120]{\frac{7}{5}}$ as $\frac{\sqrt[120]{7}}{\sqrt[120]{5}}$ .

$1 + \frac{r}{12} = \pm \frac{\sqrt[120]{7}}{\sqrt[120]{5}}$

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

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

$1 + \frac{r}{12} = \frac{\sqrt[120]{7}}{\sqrt[120]{5}}$

Subtract $1$ from both sides of the equation.

$\frac{r}{12} = \frac{\sqrt[120]{7}}{\sqrt[120]{5}} - 1$

Multiply both sides of the equation by $12$ .

$12 \cdot \frac{r}{12} = 12 \cdot (\frac{\sqrt[120]{7}}{\sqrt[120]{5}} - 1)$

Simplify both sides of the equation.

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Cancel the common factor of $12$ .

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Cancel the common factor.

$12 \cdot \frac{r}{12} = 12 \cdot (\frac{\sqrt[120]{7}}{\sqrt[120]{5}} - 1)$

Rewrite the expression.

$r = 12 \cdot (\frac{\sqrt[120]{7}}{\sqrt[120]{5}} - 1)$

Simplify $12 \cdot (\frac{\sqrt[120]{7}}{\sqrt[120]{5}} - 1)$ .

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Apply the distributive property.

$r = 12 (\frac{\sqrt[120]{7}}{\sqrt[120]{5}}) + 12 \cdot - 1$

Combine $12$ and $\frac{\sqrt[120]{7}}{\sqrt[120]{5}}$ .

$r = \frac{12 \sqrt[120]{7}}{\sqrt[120]{5}} + 12 \cdot - 1$

Multiply $12$ by $- 1$ .

$r = \frac{12 \sqrt[120]{7}}{\sqrt[120]{5}} - 12$

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

$1 + \frac{r}{12} = - \frac{\sqrt[120]{7}}{\sqrt[120]{5}}$

Subtract $1$ from both sides of the equation.

$\frac{r}{12} = - \frac{\sqrt[120]{7}}{\sqrt[120]{5}} - 1$

Multiply both sides of the equation by $12$ .

$12 \cdot \frac{r}{12} = 12 \cdot (- \frac{\sqrt[120]{7}}{\sqrt[120]{5}} - 1)$

Simplify both sides of the equation.

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Cancel the common factor of $12$ .

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Cancel the common factor.

$12 \cdot \frac{r}{12} = 12 \cdot (- \frac{\sqrt[120]{7}}{\sqrt[120]{5}} - 1)$

Rewrite the expression.

$r = 12 \cdot (- \frac{\sqrt[120]{7}}{\sqrt[120]{5}} - 1)$

Simplify $12 \cdot (- \frac{\sqrt[120]{7}}{\sqrt[120]{5}} - 1)$ .

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Apply the distributive property.

$r = 12 (- \frac{\sqrt[120]{7}}{\sqrt[120]{5}}) + 12 \cdot - 1$

Multiply $12 (- \frac{\sqrt[120]{7}}{\sqrt[120]{5}})$ .

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Multiply $- 1$ by $12$ .

$r = - 12 \frac{\sqrt[120]{7}}{\sqrt[120]{5}} + 12 \cdot - 1$

Combine $- 12$ and $\frac{\sqrt[120]{7}}{\sqrt[120]{5}}$ .

$r = \frac{- 12 \sqrt[120]{7}}{\sqrt[120]{5}} + 12 \cdot - 1$

Multiply $12$ by $- 1$ .

$r = \frac{- 12 \sqrt[120]{7}}{\sqrt[120]{5}} - 12$

Move the negative in front of the fraction.

$r = - \frac{12 \sqrt[120]{7}}{\sqrt[120]{5}} - 12$

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

$r = \frac{12 \sqrt[120]{7}}{\sqrt[120]{5}} - 12, - \frac{12 \sqrt[120]{7}}{\sqrt[120]{5}} - 12$

The result can be shown in multiple forms.

Exact Form:

$r = \frac{12 \sqrt[120]{7}}{\sqrt[120]{5}} - 12, - \frac{12 \sqrt[120]{7}}{\sqrt[120]{5}} - 12$

Decimal Form:

$r = 0.03369444 \dots, - 24.03369444 \dots$

Solve for r 7000=5000(1+r/12)^120

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