Finite Math Examples

$70000 = \frac{R ({(1 + 0.035)}^{22} - 1)}{0.035}$

Step 1

Rewrite the equation as $\frac{R ({(1 + 0.035)}^{22} - 1)}{0.035} = 70000$ .

$\frac{R ({(1 + 0.035)}^{22} - 1)}{0.035} = 70000$

Step 2

Multiply both sides of the equation by $\frac{0.035}{{(1 + 0.035)}^{22} - 1}$ .

$\frac{0.035}{{(1 + 0.035)}^{22} - 1} \cdot \frac{R ({(1 + 0.035)}^{22} - 1)}{0.035} = \frac{0.035}{{(1 + 0.035)}^{22} - 1} \cdot 70000$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{0.035}{{(1 + 0.035)}^{22} - 1} \cdot \frac{R ({(1 + 0.035)}^{22} - 1)}{0.035}$ .

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Step 3.1.1.1

Cancel the common factor of $0.035$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{0.035}{{(1 + 0.035)}^{22} - 1} \cdot \frac{R ({(1 + 0.035)}^{22} - 1)}{0.035} = \frac{0.035}{{(1 + 0.035)}^{22} - 1} \cdot 70000$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{{(1 + 0.035)}^{22} - 1} (R ({(1 + 0.035)}^{22} - 1)) = \frac{0.035}{{(1 + 0.035)}^{22} - 1} \cdot 70000$

Step 3.1.1.2

Cancel the common factor of ${(1 + 0.035)}^{22} - 1$ .

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Step 3.1.1.2.1

Factor ${(1 + 0.035)}^{22} - 1$ out of $R ({(1 + 0.035)}^{22} - 1)$ .

$\frac{1}{{(1 + 0.035)}^{22} - 1} (({(1 + 0.035)}^{22} - 1) R) = \frac{0.035}{{(1 + 0.035)}^{22} - 1} \cdot 70000$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{{(1 + 0.035)}^{22} - 1} (({(1 + 0.035)}^{22} - 1) R) = \frac{0.035}{{(1 + 0.035)}^{22} - 1} \cdot 70000$

Step 3.1.1.2.3

Rewrite the expression.

$R = \frac{0.035}{{(1 + 0.035)}^{22} - 1} \cdot 70000$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{0.035}{{(1 + 0.035)}^{22} - 1} \cdot 70000$ .

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Step 3.2.1.1

Simplify the denominator.

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Step 3.2.1.1.1

Add $1$ and $0.035$ .

$R = \frac{0.035}{{1.035}^{22} - 1} \cdot 70000$

Step 3.2.1.1.2

Raise $1.035$ to the power of $22$ .

$R = \frac{0.035}{2.13151157 - 1} \cdot 70000$

Step 3.2.1.1.3

Subtract $1$ from $2.13151157$ .

$R = \frac{0.035}{1.13151157} \cdot 70000$

Step 3.2.1.2

Simplify the expression.

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Step 3.2.1.2.1

Divide $0.035$ by $1.13151157$ .

$R = 0.03093207 \cdot 70000$

Step 3.2.1.2.2

Multiply $0.03093207$ by $70000$ .

$R = 2165.24519373$