Solve for r 1.27=(1+r/12)^84

$1.27 = {(1 + \frac{r}{12})}^{84}$

Rewrite the equation as ${(1 + \frac{r}{12})}^{84} = 1.27$ .

${(1 + \frac{r}{12})}^{84} = 1.27$

Take the 84th root of both sides of the equation to eliminate the exponent on the left side.

$1 + \frac{r}{12} = \pm \sqrt[84]{1.27}$

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

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

$1 + \frac{r}{12} = \sqrt[84]{1.27}$

Subtract $1$ from both sides of the equation.

$\frac{r}{12} = \sqrt[84]{1.27} - 1$

Multiply both sides of the equation by $12$ .

$12 \frac{r}{12} = 12 (\sqrt[84]{1.27} - 1)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$12 \frac{r}{12} = 12 (\sqrt[84]{1.27} - 1)$

Rewrite the expression.

$r = 12 (\sqrt[84]{1.27} - 1)$

Simplify the right side.

Simplify $12 (\sqrt[84]{1.27} - 1)$ .

Apply the distributive property.

$r = 12 \sqrt[84]{1.27} + 12 \cdot - 1$

Multiply $12$ by $- 1$ .

$r = 12 \sqrt[84]{1.27} - 12$

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

$1 + \frac{r}{12} = - \sqrt[84]{1.27}$

Subtract $1$ from both sides of the equation.

$\frac{r}{12} = - \sqrt[84]{1.27} - 1$

Multiply both sides of the equation by $12$ .

$12 \frac{r}{12} = 12 (- \sqrt[84]{1.27} - 1)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$12 \frac{r}{12} = 12 (- \sqrt[84]{1.27} - 1)$

Rewrite the expression.

$r = 12 (- \sqrt[84]{1.27} - 1)$

Simplify the right side.

Simplify $12 (- \sqrt[84]{1.27} - 1)$ .

Apply the distributive property.

$r = 12 (- \sqrt[84]{1.27}) + 12 \cdot - 1$

Multiply.

Multiply $- 1$ by $12$ .

$r = - 12 \sqrt[84]{1.27} + 12 \cdot - 1$

Multiply $12$ by $- 1$ .

$r = - 12 \sqrt[84]{1.27} - 12$

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

$r = 12 \sqrt[84]{1.27} - 12, - 12 \sqrt[84]{1.27} - 12$

The result can be shown in multiple forms.

Exact Form:

$r = 12 \sqrt[84]{1.27} - 12, - 12 \sqrt[84]{1.27} - 12$

Decimal Form:

$r = 0.03419389 \dots, - 24.03419389 \dots$

Solve for r 1.27=(1+r/12)^84

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