Solve 26,000(.0032/12)/1-(1+frac{.0652{12})(-12)(5)}

$$\frac { 26,000 ( \frac { .0032 } { 12 } ) } { 1 - ( 1 + \frac { .0652 } { 12 } ) ( - 12 ) ( 5 ) }$$

Evaluate

$$\frac{10400}{91989}\approx 0.113056996$$

Solution Steps

Expand \frac{0.0032}{12} by multiplying both numerator and the denominator by 10000.

$$\frac{26000\times \frac{32}{120000}}{1-\left(1+\frac{0.0652}{12}\right)\left(-12\right)\times 5}$$

Reduce the fraction \frac{32}{120000} to lowest terms by extracting and canceling out 32.

$$\frac{26000\times \frac{1}{3750}}{1-\left(1+\frac{0.0652}{12}\right)\left(-12\right)\times 5}$$

Multiply 26000 and \frac{1}{3750} to get \frac{26000}{3750}.

$$\frac{\frac{26000}{3750}}{1-\left(1+\frac{0.0652}{12}\right)\left(-12\right)\times 5}$$

Reduce the fraction \frac{26000}{3750} to lowest terms by extracting and canceling out 250.

$$\frac{\frac{104}{15}}{1-\left(1+\frac{0.0652}{12}\right)\left(-12\right)\times 5}$$

Expand \frac{0.0652}{12} by multiplying both numerator and the denominator by 10000.

$$\frac{\frac{104}{15}}{1-\left(1+\frac{652}{120000}\right)\left(-12\right)\times 5}$$

Reduce the fraction \frac{652}{120000} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{104}{15}}{1-\left(1+\frac{163}{30000}\right)\left(-12\right)\times 5}$$

Convert 1 to fraction \frac{30000}{30000}.

$$\frac{\frac{104}{15}}{1-\left(\frac{30000}{30000}+\frac{163}{30000}\right)\left(-12\right)\times 5}$$

Since \frac{30000}{30000} and \frac{163}{30000} have the same denominator, add them by adding their numerators.

$$\frac{\frac{104}{15}}{1-\frac{30000+163}{30000}\left(-12\right)\times 5}$$

Add 30000 and 163 to get 30163.

$$\frac{\frac{104}{15}}{1-\frac{30163}{30000}\left(-12\right)\times 5}$$

Express \frac{30163}{30000}\left(-12\right) as a single fraction.

$$\frac{\frac{104}{15}}{1-\frac{30163\left(-12\right)}{30000}\times 5}$$

Multiply 30163 and -12 to get -361956.

$$\frac{\frac{104}{15}}{1-\frac{-361956}{30000}\times 5}$$

Reduce the fraction \frac{-361956}{30000} to lowest terms by extracting and canceling out 12.

$$\frac{\frac{104}{15}}{1-\left(-\frac{30163}{2500}\times 5\right)}$$

Express -\frac{30163}{2500}\times 5 as a single fraction.

$$\frac{\frac{104}{15}}{1-\frac{-30163\times 5}{2500}}$$

Multiply -30163 and 5 to get -150815.

$$\frac{\frac{104}{15}}{1-\frac{-150815}{2500}}$$

Reduce the fraction \frac{-150815}{2500} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{104}{15}}{1-\left(-\frac{30163}{500}\right)}$$

The opposite of -\frac{30163}{500} is \frac{30163}{500}.

$$\frac{\frac{104}{15}}{1+\frac{30163}{500}}$$

Convert 1 to fraction \frac{500}{500}.

$$\frac{\frac{104}{15}}{\frac{500}{500}+\frac{30163}{500}}$$

Since \frac{500}{500} and \frac{30163}{500} have the same denominator, add them by adding their numerators.

$$\frac{\frac{104}{15}}{\frac{500+30163}{500}}$$

Add 500 and 30163 to get 30663.

$$\frac{\frac{104}{15}}{\frac{30663}{500}}$$

Divide \frac{104}{15} by \frac{30663}{500} by multiplying \frac{104}{15} by the reciprocal of \frac{30663}{500}.

$$\frac{104}{15}\times \frac{500}{30663}$$

Multiply \frac{104}{15} times \frac{500}{30663} by multiplying numerator times numerator and denominator times denominator.

$$\frac{104\times 500}{15\times 30663}$$

Do the multiplications in the fraction \frac{104\times 500}{15\times 30663}.

$$\frac{52000}{459945}$$

Reduce the fraction \frac{52000}{459945} to lowest terms by extracting and canceling out 5.

$$\frac{10400}{91989}$$

Factor

$$\frac{13 \cdot 2 ^ {5} \cdot 5 ^ {2}}{3407 \cdot 3 ^ {3}} = 0.11305699594516735$$