Solve 80/0.07left(1-1/1+0.079right)+1000/left(1+0.07right)^9

$$\frac{ 80 }{ 0.07 } \left( 1- \frac{ 1 }{ 1+0.07 } 9 \right) + \frac{ 1000 }{ { \left(1+0.07 \right) }^{ 9 } }$$

Evaluate

$$-\frac{102001731248537011144000}{12869214486941081549}\approx -7926.026204011$$

Solution Steps

Expand \frac{80}{0.07} by multiplying both numerator and the denominator by 100.

$$\frac{8000}{7}\left(1-\frac{1}{1+0.07}\times 9\right)+\frac{1000}{\left(1+0.07\right)^{9}}$$

Add 1 and 0.07 to get 1.07.

$$\frac{8000}{7}\left(1-\frac{1}{1.07}\times 9\right)+\frac{1000}{\left(1+0.07\right)^{9}}$$

Expand \frac{1}{1.07} by multiplying both numerator and the denominator by 100.

$$\frac{8000}{7}\left(1-\frac{100}{107}\times 9\right)+\frac{1000}{\left(1+0.07\right)^{9}}$$

Multiply \frac{100}{107} and 9 to get \frac{900}{107}.

$$\frac{8000}{7}\left(1-\frac{900}{107}\right)+\frac{1000}{\left(1+0.07\right)^{9}}$$

Subtract \frac{900}{107} from 1 to get -\frac{793}{107}.

$$\frac{8000}{7}\left(-\frac{793}{107}\right)+\frac{1000}{\left(1+0.07\right)^{9}}$$

Multiply \frac{8000}{7} and -\frac{793}{107} to get -\frac{6344000}{749}.

$$-\frac{6344000}{749}+\frac{1000}{\left(1+0.07\right)^{9}}$$

Add 1 and 0.07 to get 1.07.

$$-\frac{6344000}{749}+\frac{1000}{1.07^{9}}$$

Calculate 1.07 to the power of 9 and get 1.838459212420154507.

$$-\frac{6344000}{749}+\frac{1000}{1.838459212420154507}$$

Expand \frac{1000}{1.838459212420154507} by multiplying both numerator and the denominator by 1000000000000000000.

$$-\frac{6344000}{749}+\frac{1000000000000000000000}{1838459212420154507}$$

Add -\frac{6344000}{749} and \frac{1000000000000000000000}{1838459212420154507} to get -\frac{102001731248537011144000}{12869214486941081549}.

$$-\frac{102001731248537011144000}{12869214486941081549}$$

Factor

$$-\frac{102001731248537011144000}{12869214486941081549} = -7926\frac{3.3722504199479295 \times 10^{17}}{1.286921448694108 \times 10^{19}} = -7926.026204011312$$