Basic Math Examples

\frac{195000 \cdot (\frac{0.065}{12})}{1 - {(1 + \frac{0.065}{12})}^{- 12 \cdot 15}}

$\frac{195000 \cdot (\frac{0.065}{12})}{1 - {(1 + \frac{0.065}{12})}^{- 12 \cdot 15}}$

Step 1

Combine

195000

$195000$ and

\frac{0.065}{12}

$\frac{0.065}{12}$ .

\frac{\frac{195000 \cdot 0.065}{12}}{1 - {(1 + \frac{0.065}{12})}^{- 12 \cdot 15}}

$\frac{\frac{195000 \cdot 0.065}{12}}{1 - {(1 + \frac{0.065}{12})}^{- 12 \cdot 15}}$

Step 2

Simplify the denominator.

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Step 2.1

Divide

0.065

$0.065$ by

12

$12$ .

\frac{\frac{195000 \cdot 0.065}{12}}{1 - {(1 + 0.00541 ¯ 6)}^{- 12 \cdot 15}}

$\frac{\frac{195000 \cdot 0.065}{12}}{1 - {(1 + 0.00541\overline{6})}^{- 12 \cdot 15}}$

Step 2.2

Add

1

$1$ and

0.00541 ¯ 6

$0.00541\overline{6}$ .

\frac{\frac{195000 \cdot 0.065}{12}}{1 - {1.00541 ¯ 6}^{- 12 \cdot 15}}

$\frac{\frac{195000 \cdot 0.065}{12}}{1 - {1.00541\overline{6}}^{- 12 \cdot 15}}$

Step 2.3

Multiply

- 12

$- 12$ by

15

$15$ .

\frac{\frac{195000 \cdot 0.065}{12}}{1 - {1.00541 ¯ 6}^{- 180}}

$\frac{\frac{195000 \cdot 0.065}{12}}{1 - {1.00541\overline{6}}^{- 180}}$

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{195000 \cdot 0.065}{12}}{1 - \frac{1}{{1.00541 ¯ 6}^{180}}}

$\frac{\frac{195000 \cdot 0.065}{12}}{1 - \frac{1}{{1.00541\overline{6}}^{180}}}$

Step 2.5

Raise

1.00541 ¯ 6

$1.00541\overline{6}$ to the power of

180

$180$ .

\frac{\frac{195000 \cdot 0.065}{12}}{1 - \frac{1}{2.64420081}}

$\frac{\frac{195000 \cdot 0.065}{12}}{1 - \frac{1}{2.64420081}}$

Step 2.6

Divide

1

$1$ by

2.64420081

$2.64420081$ .

\frac{\frac{195000 \cdot 0.065}{12}}{1 - 1 \cdot 0.3781861}

$\frac{\frac{195000 \cdot 0.065}{12}}{1 - 1 \cdot 0.3781861}$

Step 2.7

Multiply

- 1

$- 1$ by

0.3781861

$0.3781861$ .

\frac{\frac{195000 \cdot 0.065}{12}}{1 - 0.3781861}

$\frac{\frac{195000 \cdot 0.065}{12}}{1 - 0.3781861}$

Step 2.8

Subtract

0.3781861

$0.3781861$ from

1

$1$ .

\frac{\frac{195000 \cdot 0.065}{12}}{0.62181389}

$\frac{\frac{195000 \cdot 0.065}{12}}{0.62181389}$

\frac{\frac{195000 \cdot 0.065}{12}}{0.62181389}

$\frac{\frac{195000 \cdot 0.065}{12}}{0.62181389}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply

195000

$195000$ by

0.065

$0.065$ .

\frac{\frac{12675}{12}}{0.62181389}

$\frac{\frac{12675}{12}}{0.62181389}$

Step 3.2

Cancel the common factor of

12675

$12675$ and

12

$12$ .

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Step 3.2.1

Factor

3

$3$ out of

12675

$12675$ .

\frac{\frac{3 (4225)}{12}}{0.62181389}

$\frac{\frac{3 (4225)}{12}}{0.62181389}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor

3

$3$ out of

12

$12$ .

\frac{\frac{3 \cdot 4225}{3 \cdot 4}}{0.62181389}

$\frac{\frac{3 \cdot 4225}{3 \cdot 4}}{0.62181389}$

Step 3.2.2.2

Cancel the common factor.

$\frac{\frac{3 \cdot 4225}{3 \cdot 4}}{0.62181389}$

Step 3.2.2.3

Rewrite the expression.

$\frac{\frac{4225}{4}}{0.62181389}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4225}{4} \cdot \frac{1}{0.62181389}$

Step 5

Divide

$1$ by

$0.62181389$ .

$\frac{4225}{4} \cdot 1.60819821$

Step 6

Multiply

$\frac{4225}{4} \cdot 1.60819821$ .

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Step 6.1

Combine

$\frac{4225}{4}$ and

$1.60819821$ .

$\frac{4225 \cdot 1.60819821}{4}$

Step 6.2

Multiply

$4225$ by

$1.60819821$ .

$\frac{6794.63744931}{4}$

Step 7

Divide

$6794.63744931$ by

$4$ .

$1698.65936232$