Basic Math Examples

$p = \frac{A (0.06 \cdot 31)}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}$

Step 1

Rewrite the equation as $\frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = p$ .

$\frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = p$

Step 2

Multiply both sides of the equation by $\frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}}$ .

$\frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} \cdot \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

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 $\frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} \cdot \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}$ .

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Step 3.1.1.1

Simplify the denominator.

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Step 3.1.1.1.1

Divide $0.06$ by $31$ .

$\frac{1}{0.06 \frac{31}{{(1 + 0.00193548)}^{12 \cdot 31} - 1}} \cdot \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.1.2

Add $1$ and $0.00193548$ .

$\frac{1}{0.06 \frac{31}{{1.00193548}^{12 \cdot 31} - 1}} \cdot \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.1.3

Multiply $12$ by $31$ .

$\frac{1}{0.06 \frac{31}{{1.00193548}^{372} - 1}} \cdot \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.1.4

Raise $1.00193548$ to the power of $372$ .

$\frac{1}{0.06 \frac{31}{2.05300407 - 1}} \cdot \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.1.5

Subtract $1$ from $2.05300407$ .

$\frac{1}{0.06 (\frac{31}{1.05300407})} \cdot \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.2

Combine fractions.

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Step 3.1.1.2.1

Combine $0.06$ and $\frac{31}{1.05300407}$ .

$\frac{1}{\frac{0.06 \cdot 31}{1.05300407}} \cdot \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.2.2

Simplify the expression.

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Step 3.1.1.2.2.1

Multiply $0.06$ by $31$ .

$\frac{1}{\frac{1.86}{1.05300407}} \cdot \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.2.2.2

Divide $1.86$ by $1.05300407$ .

$\frac{1}{1.76637492} \cdot \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.2.2.3

Divide $1$ by $1.76637492$ .

$0.56613122 \frac{A \cdot 0.06 \cdot 31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.2.2.4

Multiply $31$ by $0.06$ .

$0.56613122 \frac{A \cdot 1.86}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.3

Simplify the denominator.

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Step 3.1.1.3.1

Divide $0.06$ by $31$ .

$0.56613122 \frac{A \cdot 1.86}{{(1 + 0.00193548)}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.3.2

Add $1$ and $0.00193548$ .

$0.56613122 \frac{A \cdot 1.86}{{1.00193548}^{12 \cdot 31} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.3.3

Multiply $12$ by $31$ .

$0.56613122 \frac{A \cdot 1.86}{{1.00193548}^{372} - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.3.4

Raise $1.00193548$ to the power of $372$ .

$0.56613122 \frac{A \cdot 1.86}{2.05300407 - 1} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.3.5

Subtract $1$ from $2.05300407$ .

$0.56613122 \frac{A \cdot 1.86}{1.05300407} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.4

Simplify with factoring out.

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Step 3.1.1.4.1

Move $1.86$ to the left of $A$ .

$0.56613122 \frac{1.86 \cdot A}{1.05300407} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.4.2

Factor $1.86$ out of $1.86 \cdot A$ .

$0.56613122 \frac{1.86 (A)}{1.05300407} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.4.3

Factor $1.05300407$ out of $1.05300407$ .

$0.56613122 \frac{1.86 (A)}{1.05300407 (1)} = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.5

Separate fractions.

$0.56613122 (\frac{1.86}{1.05300407} \cdot \frac{A}{1}) = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.6

Divide $1.86$ by $1.05300407$ .

$0.56613122 (1.76637492 \frac{A}{1}) = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.7

Divide $A$ by $1$ .

$0.56613122 (1.76637492 A) = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.1.1.8

Multiply $1.76637492$ by $0.56613122$ .

$1 A = \frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{0.06 \frac{31}{{(1 + \frac{0.06}{31})}^{12 \cdot 31} - 1}} p$ .

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Step 3.2.1.1

Simplify the denominator.

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Step 3.2.1.1.1

Divide $0.06$ by $31$ .

$1 A = \frac{1}{0.06 \frac{31}{{(1 + 0.00193548)}^{12 \cdot 31} - 1}} p$

Step 3.2.1.1.2

Add $1$ and $0.00193548$ .

$1 A = \frac{1}{0.06 \frac{31}{{1.00193548}^{12 \cdot 31} - 1}} p$

Step 3.2.1.1.3

Multiply $12$ by $31$ .

$1 A = \frac{1}{0.06 \frac{31}{{1.00193548}^{372} - 1}} p$

Step 3.2.1.1.4

Raise $1.00193548$ to the power of $372$ .

$1 A = \frac{1}{0.06 \frac{31}{2.05300407 - 1}} p$

Step 3.2.1.1.5

Subtract $1$ from $2.05300407$ .

$1 A = \frac{1}{0.06 (\frac{31}{1.05300407})} p$

Step 3.2.1.2

Combine fractions.

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Step 3.2.1.2.1

Combine $0.06$ and $\frac{31}{1.05300407}$ .

$1 A = \frac{1}{\frac{0.06 \cdot 31}{1.05300407}} p$

Step 3.2.1.2.2

Simplify the expression.

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Step 3.2.1.2.2.1

Multiply $0.06$ by $31$ .

$1 A = \frac{1}{\frac{1.86}{1.05300407}} p$

Step 3.2.1.2.2.2

Divide $1.86$ by $1.05300407$ .

$1 A = \frac{1}{1.76637492} p$

Step 3.2.1.2.2.3

Divide $1$ by $1.76637492$ .

$1 A = 0.56613122 p$

Step 4

Divide each term in $1 A = 0.56613122 p$ by $1$ and simplify.

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Step 4.1

Divide each term in $1 A = 0.56613122 p$ by $1$ .

$\frac{1 A}{1} = \frac{0.56613122 p}{1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $1$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{1 A}{1} = \frac{0.56613122 p}{1}$

Step 4.2.1.2

Divide $A$ by $1$ .

$A = \frac{0.56613122 p}{1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Factor $0.56613122$ out of $0.56613122 p$ .

$A = \frac{0.56613122 (p)}{1}$

Step 4.3.2

Factor $1$ out of $1$ .

$A = \frac{0.56613122 (p)}{1 (1)}$

Step 4.3.3

Separate fractions.

$A = \frac{0.56613122}{1} \cdot \frac{p}{1}$

Step 4.3.4

Divide $0.56613122$ by $1$ .

$A = 0.56613122 \frac{p}{1}$

Step 4.3.5

Divide $p$ by $1$ .

$A = 0.56613122 p$