Solve -(1+0.10/13)^12-1

$$- ( 1 + \frac { 0.10 } { 13 } ) ^ { 12 } - 1$$

Evaluate

$$-\frac{48840123192417263923006961}{23298085122481000000000000}\approx -2.096314909$$

Solution Steps

Expand \frac{0.1}{13} by multiplying both numerator and the denominator by 10.

$$-\left(1+\frac{1}{130}\right)^{12}-1$$

Add 1 and \frac{1}{130} to get \frac{131}{130}.

$$-\left(\frac{131}{130}\right)^{12}-1$$

Calculate \frac{131}{130} to the power of 12 and get \frac{25542038069936263923006961}{23298085122481000000000000}.

$$-\frac{25542038069936263923006961}{23298085122481000000000000}-1$$

Subtract 1 from -\frac{25542038069936263923006961}{23298085122481000000000000} to get -\frac{48840123192417263923006961}{23298085122481000000000000}.

$$-\frac{48840123192417263923006961}{23298085122481000000000000}$$

Factor

$$-\frac{48840123192417263923006961}{23298085122481000000000000} = -2\frac{2.243952947455268 \times 10^{24}}{2.3298085122481 \times 10^{25}} = -2.0963149089574755$$