Evaluate (188000(0.10/12))/(1-(1+0.10/12)^(-12*30))

$\frac{188000 (\frac{0.1}{12})}{1 - {(1 + \frac{0.1}{12})}^{- 12 \cdot 30}}$

Step 1

Combine $188000$ and $\frac{0.1}{12}$ .

$\frac{\frac{188000 \cdot 0.1}{12}}{1 - {(1 + \frac{0.1}{12})}^{- 12 \cdot 30}}$

Step 2

Simplify the denominator.

Divide $0.1$ by $12$ .

$\frac{\frac{188000 \cdot 0.1}{12}}{1 - {(1 + 0.008\overline{3})}^{- 12 \cdot 30}}$

Add $1$ and $0.008\overline{3}$ .

$\frac{\frac{188000 \cdot 0.1}{12}}{1 - {1.008\overline{3}}^{- 12 \cdot 30}}$

Multiply $- 12$ by $30$ .

$\frac{\frac{188000 \cdot 0.1}{12}}{1 - {1.008\overline{3}}^{- 360}}$

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

$\frac{\frac{188000 \cdot 0.1}{12}}{1 - \frac{1}{{1.008\overline{3}}^{360}}}$

Raise $1.008\overline{3}$ to the power of $360$ .

$\frac{\frac{188000 \cdot 0.1}{12}}{1 - \frac{1}{19.83739937}}$

Divide $1$ by $19.83739937$ .

$\frac{\frac{188000 \cdot 0.1}{12}}{1 - 1 \cdot 0.05040983}$

Multiply $- 1$ by $0.05040983$ .

$\frac{\frac{188000 \cdot 0.1}{12}}{1 - 0.05040983}$

Subtract $0.05040983$ from $1$ .

$\frac{\frac{188000 \cdot 0.1}{12}}{0.94959016}$

Step 3

Reduce the expression by cancelling the common factors.

Multiply $188000$ by $0.1$ .

$\frac{\frac{18800}{12}}{0.94959016}$

Cancel the common factor of $18800$ and $12$ .

Factor $4$ out of $18800$ .

$\frac{\frac{4 (4700)}{12}}{0.94959016}$

Cancel the common factors.

Factor $4$ out of $12$ .

$\frac{\frac{4 \cdot 4700}{4 \cdot 3}}{0.94959016}$

Cancel the common factor.

$\frac{\frac{4 \cdot 4700}{4 \cdot 3}}{0.94959016}$

Rewrite the expression.

$\frac{\frac{4700}{3}}{0.94959016}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4700}{3} \cdot \frac{1}{0.94959016}$

Step 5

Divide $1$ by $0.94959016$ .

$\frac{4700}{3} \cdot 1.05308588$

Step 6

Multiply $\frac{4700}{3} \cdot 1.05308588$ .

Combine $\frac{4700}{3}$ and $1.05308588$ .

$\frac{4700 \cdot 1.05308588}{3}$

Multiply $4700$ by $1.05308588$ .

$\frac{4949.5036553}{3}$

Step 7

Divide $4949.5036553$ by $3$ .

$1649.83455176$

Evaluate (188000(0.10/12))/(1-(1+0.10/12)^(-12*30))

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