Finite Math Examples

$\frac{3370}{3000} = \frac{5000 {(1 + r)}^{2}}{5000}$

Step 1

Rewrite the equation as $\frac{5000 {(1 + r)}^{2}}{5000} = \frac{3370}{3000}$ .

$\frac{5000 {(1 + r)}^{2}}{5000} = \frac{3370}{3000}$

Step 2

Cancel the common factor of $5000$ .

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Step 2.1

Cancel the common factor.

$\frac{5000 {(1 + r)}^{2}}{5000} = \frac{3370}{3000}$

Step 2.2

Divide ${(1 + r)}^{2}$ by $1$ .

${(1 + r)}^{2} = \frac{3370}{3000}$

Step 3

Solve for $r$ .

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Step 3.1

Reduce the expression $\frac{3370}{3000}$ by cancelling the common factors.

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Step 3.1.1

Factor $10$ out of $3370$ .

${(1 + r)}^{2} = \frac{10 (337)}{3000}$

Step 3.1.2

Factor $10$ out of $3000$ .

${(1 + r)}^{2} = \frac{10 \cdot 337}{10 \cdot 300}$

Step 3.1.3

Cancel the common factor.

${(1 + r)}^{2} = \frac{10 \cdot 337}{10 \cdot 300}$

Step 3.1.4

Rewrite the expression.

${(1 + r)}^{2} = \frac{337}{300}$

Step 3.2

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

$1 + r = \pm \sqrt{\frac{337}{300}}$

Step 3.3

Simplify $\pm \sqrt{\frac{337}{300}}$ .

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Step 3.3.1

Rewrite $\sqrt{\frac{337}{300}}$ as $\frac{\sqrt{337}}{\sqrt{300}}$ .

$1 + r = \pm \frac{\sqrt{337}}{\sqrt{300}}$

Step 3.3.2

Simplify the denominator.

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Step 3.3.2.1

Rewrite $300$ as $10^{2} \cdot 3$ .

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Step 3.3.2.1.1

Factor $100$ out of $300$ .

$1 + r = \pm \frac{\sqrt{337}}{\sqrt{100 (3)}}$

Step 3.3.2.1.2

Rewrite $100$ as $10^{2}$ .

$1 + r = \pm \frac{\sqrt{337}}{\sqrt{10^{2} \cdot 3}}$

Step 3.3.2.2

Pull terms out from under the radical.

$1 + r = \pm \frac{\sqrt{337}}{10 \sqrt{3}}$

Step 3.3.3

Multiply $\frac{\sqrt{337}}{10 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$1 + r = \pm \frac{\sqrt{337}}{10 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 3.3.4

Combine and simplify the denominator.

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Step 3.3.4.1

Multiply $\frac{\sqrt{337}}{10 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 \sqrt{3} \sqrt{3}}$

Step 3.3.4.2

Move $\sqrt{3}$ .

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 (\sqrt{3} \sqrt{3})}$

Step 3.3.4.3

Raise $\sqrt{3}$ to the power of $1$ .

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 ({\sqrt{3}}^{1} \sqrt{3})}$

Step 3.3.4.4

Raise $\sqrt{3}$ to the power of $1$ .

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}$

Step 3.3.4.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 {\sqrt{3}}^{1 + 1}}$

Step 3.3.4.6

Add $1$ and $1$ .

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 {\sqrt{3}}^{2}}$

Step 3.3.4.7

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 3.3.4.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 {(3^{\frac{1}{2}})}^{2}}$

Step 3.3.4.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 \cdot 3^{\frac{1}{2} \cdot 2}}$

Step 3.3.4.7.3

Combine $\frac{1}{2}$ and $2$ .

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 \cdot 3^{\frac{2}{2}}}$

Step 3.3.4.7.4

Cancel the common factor of $2$ .

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Step 3.3.4.7.4.1

Cancel the common factor.

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 \cdot 3^{\frac{2}{2}}}$

Step 3.3.4.7.4.2

Rewrite the expression.

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 \cdot 3^{1}}$

Step 3.3.4.7.5

Evaluate the exponent.

$1 + r = \pm \frac{\sqrt{337} \sqrt{3}}{10 \cdot 3}$

Step 3.3.5

Simplify the numerator.

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Step 3.3.5.1

Combine using the product rule for radicals.

$1 + r = \pm \frac{\sqrt{337 \cdot 3}}{10 \cdot 3}$

Step 3.3.5.2

Multiply $337$ by $3$ .

$1 + r = \pm \frac{\sqrt{1011}}{10 \cdot 3}$

Step 3.3.6

Multiply $10$ by $3$ .

$1 + r = \pm \frac{\sqrt{1011}}{30}$

Step 3.4

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

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Step 3.4.1

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

$1 + r = \frac{\sqrt{1011}}{30}$

Step 3.4.2

Subtract $1$ from both sides of the equation.

$r = \frac{\sqrt{1011}}{30} - 1$

Step 3.4.3

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

$1 + r = - \frac{\sqrt{1011}}{30}$

Step 3.4.4

Subtract $1$ from both sides of the equation.

$r = - \frac{\sqrt{1011}}{30} - 1$

Step 3.4.5

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

$r = \frac{\sqrt{1011}}{30} - 1, - \frac{\sqrt{1011}}{30} - 1$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = \frac{\sqrt{1011}}{30} - 1, - \frac{\sqrt{1011}}{30} - 1$

Decimal Form:

$r = 0.05987420 \dots, - 2.05987420 \dots$