Basic Math Examples

$3000 = \frac{0.02 y}{{(1 + 0.02)}^{20} - 1}$

Step 1

Rewrite the equation as $\frac{0.02 y}{{(1 + 0.02)}^{20} - 1} = 3000$ .

$\frac{0.02 y}{{(1 + 0.02)}^{20} - 1} = 3000$

Step 2

Multiply both sides of the equation by $\frac{{(1 + 0.02)}^{20} - 1}{0.02}$ .

$\frac{{(1 + 0.02)}^{20} - 1}{0.02} \cdot \frac{0.02 y}{{(1 + 0.02)}^{20} - 1} = \frac{{(1 + 0.02)}^{20} - 1}{0.02} \cdot 3000$

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 $\frac{{(1 + 0.02)}^{20} - 1}{0.02} \cdot \frac{0.02 y}{{(1 + 0.02)}^{20} - 1}$ .

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Step 3.1.1.1

Cancel the common factor of ${(1 + 0.02)}^{20} - 1$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{{(1 + 0.02)}^{20} - 1}{0.02} \cdot \frac{0.02 y}{{(1 + 0.02)}^{20} - 1} = \frac{{(1 + 0.02)}^{20} - 1}{0.02} \cdot 3000$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{0.02} (0.02 y) = \frac{{(1 + 0.02)}^{20} - 1}{0.02} \cdot 3000$

Step 3.1.1.2

Cancel the common factor of $0.02$ .

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Step 3.1.1.2.1

Factor $0.02$ out of $0.02 y$ .

$\frac{1}{0.02} (0.02 (y)) = \frac{{(1 + 0.02)}^{20} - 1}{0.02} \cdot 3000$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{0.02} (0.02 y) = \frac{{(1 + 0.02)}^{20} - 1}{0.02} \cdot 3000$

Step 3.1.1.2.3

Rewrite the expression.

$y = \frac{{(1 + 0.02)}^{20} - 1}{0.02} \cdot 3000$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{{(1 + 0.02)}^{20} - 1}{0.02} \cdot 3000$ .

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Step 3.2.1.1

Simplify the numerator.

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Step 3.2.1.1.1

Add $1$ and $0.02$ .

$y = \frac{{1.02}^{20} - 1}{0.02} \cdot 3000$

Step 3.2.1.1.2

Raise $1.02$ to the power of $20$ .

$y = \frac{1.48594739 - 1}{0.02} \cdot 3000$

Step 3.2.1.1.3

Subtract $1$ from $1.48594739$ .

$y = \frac{0.48594739}{0.02} \cdot 3000$

Step 3.2.1.2

Reduce the expression by cancelling the common factors.

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Step 3.2.1.2.1

Cancel the common factor of $0.02$ .

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Step 3.2.1.2.1.1

Factor $0.02$ out of $3000$ .

$y = \frac{0.48594739}{0.02} \cdot (0.02 (150000))$

Step 3.2.1.2.1.2

Cancel the common factor.

$y = \frac{0.48594739}{0.02} \cdot (0.02 \cdot 150000)$

Step 3.2.1.2.1.3

Rewrite the expression.

$y = 0.48594739 \cdot 150000$

Step 3.2.1.2.2

Multiply $0.48594739$ by $150000$ .

$y = 72892.10939675$