Basic Math Examples

\frac{140000 (\frac{0.07}{12})}{1 - {(1 + \frac{0.07}{12})}^{- 12 \cdot 15}}

$\frac{140000 (\frac{0.07}{12})}{1 - {(1 + \frac{0.07}{12})}^{- 12 \cdot 15}}$

Step 1

Combine

140000

$140000$ and

\frac{0.07}{12}

$\frac{0.07}{12}$ .

\frac{\frac{140000 \cdot 0.07}{12}}{1 - {(1 + \frac{0.07}{12})}^{- 12 \cdot 15}}

$\frac{\frac{140000 \cdot 0.07}{12}}{1 - {(1 + \frac{0.07}{12})}^{- 12 \cdot 15}}$

Step 2

Simplify the denominator.

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Step 2.1

Divide

0.07

$0.07$ by

12

$12$ .

\frac{\frac{140000 \cdot 0.07}{12}}{1 - {(1 + 0.0058 ¯ 3)}^{- 12 \cdot 15}}

$\frac{\frac{140000 \cdot 0.07}{12}}{1 - {(1 + 0.0058\overline{3})}^{- 12 \cdot 15}}$

Step 2.2

Add

1

$1$ and

0.0058 ¯ 3

$0.0058\overline{3}$ .

\frac{\frac{140000 \cdot 0.07}{12}}{1 - {1.0058 ¯ 3}^{- 12 \cdot 15}}

$\frac{\frac{140000 \cdot 0.07}{12}}{1 - {1.0058\overline{3}}^{- 12 \cdot 15}}$

Step 2.3

Multiply

- 12

$- 12$ by

15

$15$ .

\frac{\frac{140000 \cdot 0.07}{12}}{1 - {1.0058 ¯ 3}^{- 180}}

$\frac{\frac{140000 \cdot 0.07}{12}}{1 - {1.0058\overline{3}}^{- 180}}$

Step 2.4

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{\frac{140000 \cdot 0.07}{12}}{1 - \frac{1}{{1.0058 ¯ 3}^{180}}}

$\frac{\frac{140000 \cdot 0.07}{12}}{1 - \frac{1}{{1.0058\overline{3}}^{180}}}$

Step 2.5

Raise

1.0058 ¯ 3

$1.0058\overline{3}$ to the power of

180

$180$ .

\frac{\frac{140000 \cdot 0.07}{12}}{1 - \frac{1}{2.84894673}}

$\frac{\frac{140000 \cdot 0.07}{12}}{1 - \frac{1}{2.84894673}}$

Step 2.6

Divide

1

$1$ by

2.84894673

$2.84894673$ .

\frac{\frac{140000 \cdot 0.07}{12}}{1 - 1 \cdot 0.35100691}

$\frac{\frac{140000 \cdot 0.07}{12}}{1 - 1 \cdot 0.35100691}$

Step 2.7

Multiply

- 1

$- 1$ by

0.35100691

$0.35100691$ .

\frac{\frac{140000 \cdot 0.07}{12}}{1 - 0.35100691}

$\frac{\frac{140000 \cdot 0.07}{12}}{1 - 0.35100691}$

Step 2.8

Subtract

0.35100691

$0.35100691$ from

1

$1$ .

\frac{\frac{140000 \cdot 0.07}{12}}{0.64899308}

$\frac{\frac{140000 \cdot 0.07}{12}}{0.64899308}$

\frac{\frac{140000 \cdot 0.07}{12}}{0.64899308}

$\frac{\frac{140000 \cdot 0.07}{12}}{0.64899308}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply

140000

$140000$ by

0.07

$0.07$ .

\frac{\frac{9800}{12}}{0.64899308}

$\frac{\frac{9800}{12}}{0.64899308}$

Step 3.2

Cancel the common factor of

9800

$9800$ and

12

$12$ .

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Step 3.2.1

Factor

4

$4$ out of

9800

$9800$ .

\frac{\frac{4 (2450)}{12}}{0.64899308}

$\frac{\frac{4 (2450)}{12}}{0.64899308}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor

4

$4$ out of

12

$12$ .

\frac{\frac{4 \cdot 2450}{4 \cdot 3}}{0.64899308}

$\frac{\frac{4 \cdot 2450}{4 \cdot 3}}{0.64899308}$

Step 3.2.2.2

Cancel the common factor.

$\frac{\frac{4 \cdot 2450}{4 \cdot 3}}{0.64899308}$

Step 3.2.2.3

Rewrite the expression.

$\frac{\frac{2450}{3}}{0.64899308}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{2450}{3} \cdot \frac{1}{0.64899308}$

Step 5

Divide

$1$ by

$0.64899308$ .

$\frac{2450}{3} \cdot 1.54084846$

Step 6

Multiply

$\frac{2450}{3} \cdot 1.54084846$ .

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Step 6.1

Combine

$\frac{2450}{3}$ and

$1.54084846$ .

$\frac{2450 \cdot 1.54084846}{3}$

Step 6.2

Multiply

$2450$ by

$1.54084846$ .

$\frac{3775.07873758}{3}$

Step 7

Divide

$3775.07873758$ by

$3$ .

$1258.35957919$