Finite Math Examples

$f v a = \frac{c ({(1 + \frac{0.108}{12})}^{120} - 1)}{\frac{0.108}{12}}$

Step 1

Simplify.

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Step 1.1

Divide $0.108$ by $12$ .

$f v a = \frac{c ({(1 + 0.009)}^{120} - 1)}{\frac{0.108}{12}}$

Step 1.2

Divide $0.108$ by $12$ .

$f v a = \frac{c ({(1 + 0.009)}^{120} - 1)}{0.009}$

Step 1.3

Add $1$ and $0.009$ .

$f v a = \frac{c ({1.009}^{120} - 1)}{0.009}$

Step 2

Divide each term in $f v a = \frac{c ({1.009}^{120} - 1)}{0.009}$ by $v a$ and simplify.

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Step 2.1

Divide each term in $f v a = \frac{c ({1.009}^{120} - 1)}{0.009}$ by $v a$ .

$\frac{f v a}{v a} = \frac{\frac{c ({1.009}^{120} - 1)}{0.009}}{v a}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $v$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{f v a}{v a} = \frac{\frac{c ({1.009}^{120} - 1)}{0.009}}{v a}$

Step 2.2.1.2

Rewrite the expression.

$\frac{f a}{a} = \frac{\frac{c ({1.009}^{120} - 1)}{0.009}}{v a}$

Step 2.2.2

Cancel the common factor of $a$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{f a}{a} = \frac{\frac{c ({1.009}^{120} - 1)}{0.009}}{v a}$

Step 2.2.2.2

Divide $f$ by $1$ .

$f = \frac{\frac{c ({1.009}^{120} - 1)}{0.009}}{v a}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$f = \frac{c ({1.009}^{120} - 1)}{0.009} \cdot \frac{1}{v a}$

Step 2.3.2

Combine fractions.

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Step 2.3.2.1

Combine.

$f = \frac{c ({1.009}^{120} - 1) \cdot 1}{0.009 (v a)}$

Step 2.3.2.2

Multiply $c$ by $1$ .

$f = \frac{c ({1.009}^{120} - 1)}{0.009 v a}$

Step 2.3.3

Simplify the numerator.

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Step 2.3.3.1

Raise $1.009$ to the power of $120$ .

$f = \frac{c (2.930488 - 1)}{0.009 v a}$

Step 2.3.3.2

Subtract $1$ from $2.930488$ .

$f = \frac{c \cdot 1.930488}{0.009 v a}$

Step 2.3.4

Simplify with factoring out.

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Step 2.3.4.1

Move $1.930488$ to the left of $c$ .

$f = \frac{1.930488 \cdot c}{0.009 v a}$

Step 2.3.4.2

Factor $1.930488$ out of $1.930488 \cdot c$ .

$f = \frac{1.930488 (c)}{0.009 v a}$

Step 2.3.4.3

Factor $0.009$ out of $0.009 v a$ .

$f = \frac{1.930488 (c)}{0.009 (v a)}$

Step 2.3.5

Separate fractions.

$f = \frac{1.930488}{0.009} \cdot \frac{c}{v a}$

Step 2.3.6

Divide $1.930488$ by $0.009$ .

$f = 214.49866748 \frac{c}{v a}$

Step 2.3.7

Combine $214.49866748$ and $\frac{c}{v a}$ .

$f = \frac{214.49866748 c}{v a}$