Finite Math Examples

$7000000 = 80000 {(1 + r)}^{40}$

Step 1

Rewrite the equation as $80000 {(1 + r)}^{40} = 7000000$ .

$80000 {(1 + r)}^{40} = 7000000$

Step 2

Divide each term in $80000 {(1 + r)}^{40} = 7000000$ by $80000$ and simplify.

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Step 2.1

Divide each term in $80000 {(1 + r)}^{40} = 7000000$ by $80000$ .

$\frac{80000 {(1 + r)}^{40}}{80000} = \frac{7000000}{80000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $80000$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{80000 {(1 + r)}^{40}}{80000} = \frac{7000000}{80000}$

Step 2.2.1.2

Divide ${(1 + r)}^{40}$ by $1$ .

${(1 + r)}^{40} = \frac{7000000}{80000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $7000000$ and $80000$ .

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Step 2.3.1.1

Factor $40000$ out of $7000000$ .

${(1 + r)}^{40} = \frac{40000 (175)}{80000}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $40000$ out of $80000$ .

${(1 + r)}^{40} = \frac{40000 \cdot 175}{40000 \cdot 2}$

Step 2.3.1.2.2

Cancel the common factor.

${(1 + r)}^{40} = \frac{40000 \cdot 175}{40000 \cdot 2}$

Step 2.3.1.2.3

Rewrite the expression.

${(1 + r)}^{40} = \frac{175}{2}$

Step 3

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

$1 + r = \pm \sqrt[40]{\frac{175}{2}}$

Step 4

Rewrite $\sqrt[40]{\frac{175}{2}}$ as $\frac{\sqrt[40]{175}}{\sqrt[40]{2}}$ .

$1 + r = \pm \frac{\sqrt[40]{175}}{\sqrt[40]{2}}$

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.

$1 + r = \frac{\sqrt[40]{175}}{\sqrt[40]{2}}$

Step 5.2

Subtract $1$ from both sides of the equation.

$r = \frac{\sqrt[40]{175}}{\sqrt[40]{2}} - 1$

Step 5.3

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

$1 + r = - \frac{\sqrt[40]{175}}{\sqrt[40]{2}}$

Step 5.4

Subtract $1$ from both sides of the equation.

$r = - \frac{\sqrt[40]{175}}{\sqrt[40]{2}} - 1$

Step 5.5

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

$r = \frac{\sqrt[40]{175}}{\sqrt[40]{2}} - 1, - \frac{\sqrt[40]{175}}{\sqrt[40]{2}} - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = \frac{\sqrt[40]{175}}{\sqrt[40]{2}} - 1, - \frac{\sqrt[40]{175}}{\sqrt[40]{2}} - 1$

Decimal Form:

$r = 0.11827908 \dots, - 2.11827908 \dots$