Basic Math Examples

\frac{160000 (\frac{0.05}{12})}{1 - {(1 + \frac{0.05}{12})}^{- 12 \cdot 20}}

$\frac{160000 (\frac{0.05}{12})}{1 - {(1 + \frac{0.05}{12})}^{- 12 \cdot 20}}$

Step 1

Combine

160000

$160000$ and

\frac{0.05}{12}

$\frac{0.05}{12}$ .

\frac{\frac{160000 \cdot 0.05}{12}}{1 - {(1 + \frac{0.05}{12})}^{- 12 \cdot 20}}

$\frac{\frac{160000 \cdot 0.05}{12}}{1 - {(1 + \frac{0.05}{12})}^{- 12 \cdot 20}}$

Step 2

Simplify the denominator.

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Step 2.1

Divide

0.05

$0.05$ by

12

$12$ .

\frac{\frac{160000 \cdot 0.05}{12}}{1 - {(1 + 0.0041 ¯ 6)}^{- 12 \cdot 20}}

$\frac{\frac{160000 \cdot 0.05}{12}}{1 - {(1 + 0.0041\overline{6})}^{- 12 \cdot 20}}$

Step 2.2

Add

1

$1$ and

0.0041 ¯ 6

$0.0041\overline{6}$ .

\frac{\frac{160000 \cdot 0.05}{12}}{1 - {1.0041 ¯ 6}^{- 12 \cdot 20}}

$\frac{\frac{160000 \cdot 0.05}{12}}{1 - {1.0041\overline{6}}^{- 12 \cdot 20}}$

Step 2.3

Multiply

- 12

$- 12$ by

20

$20$ .

\frac{\frac{160000 \cdot 0.05}{12}}{1 - {1.0041 ¯ 6}^{- 240}}

$\frac{\frac{160000 \cdot 0.05}{12}}{1 - {1.0041\overline{6}}^{- 240}}$

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{160000 \cdot 0.05}{12}}{1 - \frac{1}{{1.0041 ¯ 6}^{240}}}

$\frac{\frac{160000 \cdot 0.05}{12}}{1 - \frac{1}{{1.0041\overline{6}}^{240}}}$

Step 2.5

Raise

1.0041 ¯ 6

$1.0041\overline{6}$ to the power of

240

$240$ .

\frac{\frac{160000 \cdot 0.05}{12}}{1 - \frac{1}{2.71264028}}

$\frac{\frac{160000 \cdot 0.05}{12}}{1 - \frac{1}{2.71264028}}$

Step 2.6

Divide

1

$1$ by

2.71264028

$2.71264028$ .

\frac{\frac{160000 \cdot 0.05}{12}}{1 - 1 \cdot 0.36864452}

$\frac{\frac{160000 \cdot 0.05}{12}}{1 - 1 \cdot 0.36864452}$

Step 2.7

Multiply

- 1

$- 1$ by

0.36864452

$0.36864452$ .

\frac{\frac{160000 \cdot 0.05}{12}}{1 - 0.36864452}

$\frac{\frac{160000 \cdot 0.05}{12}}{1 - 0.36864452}$

Step 2.8

Subtract

0.36864452

$0.36864452$ from

1

$1$ .

\frac{\frac{160000 \cdot 0.05}{12}}{0.63135547}

$\frac{\frac{160000 \cdot 0.05}{12}}{0.63135547}$

\frac{\frac{160000 \cdot 0.05}{12}}{0.63135547}

$\frac{\frac{160000 \cdot 0.05}{12}}{0.63135547}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply

160000

$160000$ by

0.05

$0.05$ .

\frac{\frac{8000}{12}}{0.63135547}

$\frac{\frac{8000}{12}}{0.63135547}$

Step 3.2

Cancel the common factor of

8000

$8000$ and

12

$12$ .

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Step 3.2.1

Factor

4

$4$ out of

8000

$8000$ .

\frac{\frac{4 (2000)}{12}}{0.63135547}

$\frac{\frac{4 (2000)}{12}}{0.63135547}$

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 2000}{4 \cdot 3}}{0.63135547}

$\frac{\frac{4 \cdot 2000}{4 \cdot 3}}{0.63135547}$

Step 3.2.2.2

Cancel the common factor.

$\frac{\frac{4 \cdot 2000}{4 \cdot 3}}{0.63135547}$

Step 3.2.2.3

Rewrite the expression.

$\frac{\frac{2000}{3}}{0.63135547}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{2000}{3} \cdot \frac{1}{0.63135547}$

Step 5

Divide

$1$ by

$0.63135547$ .

$\frac{2000}{3} \cdot 1.58389377$

Step 6

Multiply

$\frac{2000}{3} \cdot 1.58389377$ .

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Step 6.1

Combine

$\frac{2000}{3}$ and

$1.58389377$ .

$\frac{2000 \cdot 1.58389377}{3}$

Step 6.2

Multiply

$2000$ by

$1.58389377$ .

$\frac{3167.78754823}{3}$

Step 7

Divide

$3167.78754823$ by

$3$ .

$1055.92918274$