Solve 12000*1/0.06left(1-1/1.06^10right)

$$12000 \times \frac{ 1 }{ 0.06 } \left( 1- \frac{ 1 }{ { 1.06 }^{ 10 } } \right)$$

Evaluate

$$\frac{15446244073102609800000}{174887470365513049}\approx 88321.044616976$$

Solution Steps

Expand \frac{1}{0.06} by multiplying both numerator and the denominator by 100.

$$12000\times \frac{100}{6}\left(1-\frac{1}{1.06^{10}}\right)$$

Reduce the fraction \frac{100}{6} to lowest terms by extracting and canceling out 2.

$$12000\times \frac{50}{3}\left(1-\frac{1}{1.06^{10}}\right)$$

Express 12000\times \frac{50}{3} as a single fraction.

$$\frac{12000\times 50}{3}\left(1-\frac{1}{1.06^{10}}\right)$$

Multiply 12000 and 50 to get 600000.

$$\frac{600000}{3}\left(1-\frac{1}{1.06^{10}}\right)$$

Divide 600000 by 3 to get 200000.

$$200000\left(1-\frac{1}{1.06^{10}}\right)$$

Calculate 1.06 to the power of 10 and get 1.79084769654285362176.

$$200000\left(1-\frac{1}{1.79084769654285362176}\right)$$

Expand \frac{1}{1.79084769654285362176} by multiplying both numerator and the denominator by 100000000000000000000.

$$200000\left(1-\frac{100000000000000000000}{179084769654285362176}\right)$$

Reduce the fraction \frac{100000000000000000000}{179084769654285362176} to lowest terms by extracting and canceling out 1024.

$$200000\left(1-\frac{97656250000000000}{174887470365513049}\right)$$

Convert 1 to fraction \frac{174887470365513049}{174887470365513049}.

$$200000\left(\frac{174887470365513049}{174887470365513049}-\frac{97656250000000000}{174887470365513049}\right)$$

Since \frac{174887470365513049}{174887470365513049} and \frac{97656250000000000}{174887470365513049} have the same denominator, subtract them by subtracting their numerators.

$$200000\times \frac{174887470365513049-97656250000000000}{174887470365513049}$$

Subtract 97656250000000000 from 174887470365513049 to get 77231220365513049.

$$200000\times \frac{77231220365513049}{174887470365513049}$$

Express 200000\times \frac{77231220365513049}{174887470365513049} as a single fraction.

$$\frac{200000\times 77231220365513049}{174887470365513049}$$

Multiply 200000 and 77231220365513049 to get 15446244073102609800000.

$$\frac{15446244073102609800000}{174887470365513049}$$

Factor

$$\frac{3 \cdot 11 \cdot 61 \cdot 103 \cdot 151 \cdot 181 \cdot 3191 \cdot 4271 \cdot 2 ^ {6} \cdot 5 ^ {5}}{53 ^ {10}} = 88321\frac{7802950133222048}{1.7488747036551306 \times 10^{17}} = 88321.04461697637$$