Solve 500000=P(1+6/1200)((1+6/1200)^12-1/frac{6{100*12}})

$$500000 = P ( 1 + \frac { 6 } { 1200 } ) ( \frac { ( 1 + \frac { 6 } { 1200 } ) ^ { 12 } - 1 } { \frac { 6 } { 100 \times 12 } } )$$

Solve for P

$$P = \frac{2048000000000000000000000000000000}{50779095796795036986291122601} = 40331\frac{2.8287419459402225 \times 10^{28}}{5.0779095796795035 \times 10^{28}} \approx 40331.557068199$$

Steps for Solving Linear Equation

Reduce the fraction \frac{6}{1200} to lowest terms by extracting and canceling out 6.

$$500000=P\left(1+\frac{1}{200}\right)\times \frac{\left(1+\frac{6}{1200}\right)^{12}-1}{\frac{6}{100\times 12}}$$

Add 1 and \frac{1}{200} to get \frac{201}{200}.

$$500000=P\times \frac{201}{200}\times \frac{\left(1+\frac{6}{1200}\right)^{12}-1}{\frac{6}{100\times 12}}$$

Reduce the fraction \frac{6}{1200} to lowest terms by extracting and canceling out 6.

$$500000=P\times \frac{201}{200}\times \frac{\left(1+\frac{1}{200}\right)^{12}-1}{\frac{6}{100\times 12}}$$

Add 1 and \frac{1}{200} to get \frac{201}{200}.

$$500000=P\times \frac{201}{200}\times \frac{\left(\frac{201}{200}\right)^{12}-1}{\frac{6}{100\times 12}}$$

Calculate \frac{201}{200} to the power of 12 and get \frac{4348632317396990233762642401}{4096000000000000000000000000}.

$$500000=P\times \frac{201}{200}\times \frac{\frac{4348632317396990233762642401}{4096000000000000000000000000}-1}{\frac{6}{100\times 12}}$$

Subtract 1 from \frac{4348632317396990233762642401}{4096000000000000000000000000} to get \frac{252632317396990233762642401}{4096000000000000000000000000}.

$$500000=P\times \frac{201}{200}\times \frac{\frac{252632317396990233762642401}{4096000000000000000000000000}}{\frac{6}{100\times 12}}$$

Multiply 100 and 12 to get 1200.

$$500000=P\times \frac{201}{200}\times \frac{\frac{252632317396990233762642401}{4096000000000000000000000000}}{\frac{6}{1200}}$$

Reduce the fraction \frac{6}{1200} to lowest terms by extracting and canceling out 6.

$$500000=P\times \frac{201}{200}\times \frac{\frac{252632317396990233762642401}{4096000000000000000000000000}}{\frac{1}{200}}$$

Divide \frac{252632317396990233762642401}{4096000000000000000000000000} by \frac{1}{200} by multiplying \frac{252632317396990233762642401}{4096000000000000000000000000} by the reciprocal of \frac{1}{200}.

$$500000=P\times \frac{201}{200}\times \frac{252632317396990233762642401}{4096000000000000000000000000}\times 200$$

Multiply \frac{252632317396990233762642401}{4096000000000000000000000000} and 200 to get \frac{252632317396990233762642401}{20480000000000000000000000}.

$$500000=P\times \frac{201}{200}\times \frac{252632317396990233762642401}{20480000000000000000000000}$$

Multiply \frac{201}{200} and \frac{252632317396990233762642401}{20480000000000000000000000} to get \frac{50779095796795036986291122601}{4096000000000000000000000000}.

$$500000=P\times \frac{50779095796795036986291122601}{4096000000000000000000000000}$$

Swap sides so that all variable terms are on the left hand side.

$$P\times \frac{50779095796795036986291122601}{4096000000000000000000000000}=500000$$

Multiply both sides by \frac{4096000000000000000000000000}{50779095796795036986291122601}, the reciprocal of \frac{50779095796795036986291122601}{4096000000000000000000000000}.

$$P=500000\times \frac{4096000000000000000000000000}{50779095796795036986291122601}$$

Multiply 500000 and \frac{4096000000000000000000000000}{50779095796795036986291122601} to get \frac{2048000000000000000000000000000000}{50779095796795036986291122601}.

$$P=\frac{2048000000000000000000000000000000}{50779095796795036986291122601}$$