Solve 26,000(.0632/12)/1-(1+frac{.0632{12})(-12)(5)}

$$\frac { 26,000 ( \frac { .0632 } { 12 } ) } { 1 - ( 1 + \frac { .0632 } { 12 } ) ( - 12 ) ( 5 ) }$$

Evaluate

$$\frac{102700}{45987}\approx 2.233239829$$

Solution Steps

Expand \frac{0.0632}{12} by multiplying both numerator and the denominator by 10000.

$$\frac{26000\times \frac{632}{120000}}{1-\left(1+\frac{0.0632}{12}\right)\left(-12\right)\times 5}$$

Reduce the fraction \frac{632}{120000} to lowest terms by extracting and canceling out 8.

$$\frac{26000\times \frac{79}{15000}}{1-\left(1+\frac{0.0632}{12}\right)\left(-12\right)\times 5}$$

Express 26000\times \frac{79}{15000} as a single fraction.

$$\frac{\frac{26000\times 79}{15000}}{1-\left(1+\frac{0.0632}{12}\right)\left(-12\right)\times 5}$$

Multiply 26000 and 79 to get 2054000.

$$\frac{\frac{2054000}{15000}}{1-\left(1+\frac{0.0632}{12}\right)\left(-12\right)\times 5}$$

Reduce the fraction \frac{2054000}{15000} to lowest terms by extracting and canceling out 1000.

$$\frac{\frac{2054}{15}}{1-\left(1+\frac{0.0632}{12}\right)\left(-12\right)\times 5}$$

Expand \frac{0.0632}{12} by multiplying both numerator and the denominator by 10000.

$$\frac{\frac{2054}{15}}{1-\left(1+\frac{632}{120000}\right)\left(-12\right)\times 5}$$

Reduce the fraction \frac{632}{120000} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{2054}{15}}{1-\left(1+\frac{79}{15000}\right)\left(-12\right)\times 5}$$

Convert 1 to fraction \frac{15000}{15000}.

$$\frac{\frac{2054}{15}}{1-\left(\frac{15000}{15000}+\frac{79}{15000}\right)\left(-12\right)\times 5}$$

Since \frac{15000}{15000} and \frac{79}{15000} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2054}{15}}{1-\frac{15000+79}{15000}\left(-12\right)\times 5}$$

Add 15000 and 79 to get 15079.

$$\frac{\frac{2054}{15}}{1-\frac{15079}{15000}\left(-12\right)\times 5}$$

Express \frac{15079}{15000}\left(-12\right) as a single fraction.

$$\frac{\frac{2054}{15}}{1-\frac{15079\left(-12\right)}{15000}\times 5}$$

Multiply 15079 and -12 to get -180948.

$$\frac{\frac{2054}{15}}{1-\frac{-180948}{15000}\times 5}$$

Reduce the fraction \frac{-180948}{15000} to lowest terms by extracting and canceling out 12.

$$\frac{\frac{2054}{15}}{1-\left(-\frac{15079}{1250}\times 5\right)}$$

Express -\frac{15079}{1250}\times 5 as a single fraction.

$$\frac{\frac{2054}{15}}{1-\frac{-15079\times 5}{1250}}$$

Multiply -15079 and 5 to get -75395.

$$\frac{\frac{2054}{15}}{1-\frac{-75395}{1250}}$$

Reduce the fraction \frac{-75395}{1250} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{2054}{15}}{1-\left(-\frac{15079}{250}\right)}$$

The opposite of -\frac{15079}{250} is \frac{15079}{250}.

$$\frac{\frac{2054}{15}}{1+\frac{15079}{250}}$$

Convert 1 to fraction \frac{250}{250}.

$$\frac{\frac{2054}{15}}{\frac{250}{250}+\frac{15079}{250}}$$

Since \frac{250}{250} and \frac{15079}{250} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2054}{15}}{\frac{250+15079}{250}}$$

Add 250 and 15079 to get 15329.

$$\frac{\frac{2054}{15}}{\frac{15329}{250}}$$

Divide \frac{2054}{15} by \frac{15329}{250} by multiplying \frac{2054}{15} by the reciprocal of \frac{15329}{250}.

$$\frac{2054}{15}\times \frac{250}{15329}$$

Multiply \frac{2054}{15} times \frac{250}{15329} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2054\times 250}{15\times 15329}$$

Do the multiplications in the fraction \frac{2054\times 250}{15\times 15329}.

$$\frac{513500}{229935}$$

Reduce the fraction \frac{513500}{229935} to lowest terms by extracting and canceling out 5.

$$\frac{102700}{45987}$$

Factor

$$\frac{13 \cdot 79 \cdot 2 ^ {2} \cdot 5 ^ {2}}{3 \cdot 15329} = 2\frac{10726}{45987} = 2.2332398286472266$$