Finite Math Examples

$\frac{83600 (\frac{0.07}{12})}{1 - {(1 + \frac{0.07}{12})}^{- 12 \cdot 30}}$

Step 1

Combine $83600$ and $\frac{0.07}{12}$ .

$\frac{\frac{83600 \cdot 0.07}{12}}{1 - {(1 + \frac{0.07}{12})}^{- 12 \cdot 30}}$

Step 2

Simplify the denominator.

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Step 2.1

Divide $0.07$ by $12$ .

$\frac{\frac{83600 \cdot 0.07}{12}}{1 - {(1 + 0.0058\overline{3})}^{- 12 \cdot 30}}$

Step 2.2

Add $1$ and $0.0058\overline{3}$ .

$\frac{\frac{83600 \cdot 0.07}{12}}{1 - {1.0058\overline{3}}^{- 12 \cdot 30}}$

Step 2.3

Multiply $- 12$ by $30$ .

$\frac{\frac{83600 \cdot 0.07}{12}}{1 - {1.0058\overline{3}}^{- 360}}$

Step 2.4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{83600 \cdot 0.07}{12}}{1 - \frac{1}{{1.0058\overline{3}}^{360}}}$

Step 2.5

Raise $1.0058\overline{3}$ to the power of $360$ .

$\frac{\frac{83600 \cdot 0.07}{12}}{1 - \frac{1}{8.11649747}}$

Step 2.6

Divide $1$ by $8.11649747$ .

$\frac{\frac{83600 \cdot 0.07}{12}}{1 - 1 \cdot 0.12320585}$

Step 2.7

Multiply $- 1$ by $0.12320585$ .

$\frac{\frac{83600 \cdot 0.07}{12}}{1 - 0.12320585}$

Step 2.8

Subtract $0.12320585$ from $1$ .

$\frac{\frac{83600 \cdot 0.07}{12}}{0.87679414}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $83600$ by $0.07$ .

$\frac{\frac{5852}{12}}{0.87679414}$

Step 3.2

Cancel the common factor of $5852$ and $12$ .

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Step 3.2.1

Factor $4$ out of $5852$ .

$\frac{\frac{4 (1463)}{12}}{0.87679414}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $4$ out of $12$ .

$\frac{\frac{4 \cdot 1463}{4 \cdot 3}}{0.87679414}$

Step 3.2.2.2

Cancel the common factor.

$\frac{\frac{4 \cdot 1463}{4 \cdot 3}}{0.87679414}$

Step 3.2.2.3

Rewrite the expression.

$\frac{\frac{1463}{3}}{0.87679414}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1463}{3} \cdot \frac{1}{0.87679414}$

Step 5

Divide $1$ by $0.87679414$ .

$\frac{1463}{3} \cdot 1.14051856$

Step 6

Multiply $\frac{1463}{3} \cdot 1.14051856$ .

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Step 6.1

Combine $\frac{1463}{3}$ and $1.14051856$ .

$\frac{1463 \cdot 1.14051856}{3}$

Step 6.2

Multiply $1463$ by $1.14051856$ .

$\frac{1668.5786579}{3}$

Step 7

Divide $1668.5786579$ by $3$ .

$556.19288596$