Solve 1200/1-(frac{1{1.06})^20}

$$\frac { 1200 } { 1 - ( \frac { 1 } { 1.06 } ) ^ { 20 } }$$

Evaluate

$$\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}\approx 1743.691139537$$

Solution Steps

Expand \frac{1}{1.06} by multiplying both numerator and the denominator by 100.

$$\frac{1200}{1-\left(\frac{100}{106}\right)^{20}}$$

Reduce the fraction \frac{100}{106} to lowest terms by extracting and canceling out 2.

$$\frac{1200}{1-\left(\frac{50}{53}\right)^{20}}$$

Calculate \frac{50}{53} to the power of 20 and get \frac{9536743164062500000000000000000000}{30585627290848204916791848989276401}.

$$\frac{1200}{1-\frac{9536743164062500000000000000000000}{30585627290848204916791848989276401}}$$

Subtract \frac{9536743164062500000000000000000000}{30585627290848204916791848989276401} from 1 to get \frac{21048884126785704916791848989276401}{30585627290848204916791848989276401}.

$$\frac{1200}{\frac{21048884126785704916791848989276401}{30585627290848204916791848989276401}}$$

Divide 1200 by \frac{21048884126785704916791848989276401}{30585627290848204916791848989276401} by multiplying 1200 by the reciprocal of \frac{21048884126785704916791848989276401}{30585627290848204916791848989276401}.

$$1200\times \frac{30585627290848204916791848989276401}{21048884126785704916791848989276401}$$

Multiply 1200 and \frac{30585627290848204916791848989276401}{21048884126785704916791848989276401} to get \frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}.

$$\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}$$

Factor

$$\frac{2 ^ {4} \cdot 5 ^ {2} \cdot 53 ^ {20}}{11 \cdot 61 \cdot 103 \cdot 151 \cdot 181 \cdot 3191 \cdot 4271 \cdot 5309 \cdot 51336168838861} = 1743\frac{4.8492386767866735 \times 10^{33}}{7.0162947089285685 \times 10^{33}} = 1743.691139537029$$