Solve 80/8.07[1-1/(1+0.07)9]+1000/(1+0.07)^9

$$\frac { 80 } { 8.07 } [ 1 - \frac { 1 } { ( 1 + 0.07 ) } 9 ] + \frac { 1000 } { ( 1 + 0.07 ) ^ { 9 } }$$

Evaluate

$$\frac{697998268751462988856000}{1483636584423064687149}\approx 470.464449367$$

Solution Steps

Expand \frac{80}{8.07} by multiplying both numerator and the denominator by 100.

$$\frac{8000}{807}\left(1-\frac{1}{1+0.07}\times 9\right)+\frac{1000}{\left(1+0.07\right)^{9}}$$

Add 1 and 0.07 to get 1.07.

$$\frac{8000}{807}\left(1-\frac{1}{1.07}\times 9\right)+\frac{1000}{\left(1+0.07\right)^{9}}$$

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

$$\frac{8000}{807}\left(1-\frac{100}{107}\times 9\right)+\frac{1000}{\left(1+0.07\right)^{9}}$$

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

$$\frac{8000}{807}\left(1-\frac{900}{107}\right)+\frac{1000}{\left(1+0.07\right)^{9}}$$

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

$$\frac{8000}{807}\left(-\frac{793}{107}\right)+\frac{1000}{\left(1+0.07\right)^{9}}$$

Multiply \frac{8000}{807} and -\frac{793}{107} to get -\frac{6344000}{86349}.

$$-\frac{6344000}{86349}+\frac{1000}{\left(1+0.07\right)^{9}}$$

Add 1 and 0.07 to get 1.07.

$$-\frac{6344000}{86349}+\frac{1000}{1.07^{9}}$$

Calculate 1.07 to the power of 9 and get 1.838459212420154507.

$$-\frac{6344000}{86349}+\frac{1000}{1.838459212420154507}$$

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

$$-\frac{6344000}{86349}+\frac{1000000000000000000000}{1838459212420154507}$$

Add -\frac{6344000}{86349} and \frac{1000000000000000000000}{1838459212420154507} to get \frac{697998268751462988856000}{1483636584423064687149}.

$$\frac{697998268751462988856000}{1483636584423064687149}$$

Factor

$$\frac{280175369 \cdot 311411327503 \cdot 2 ^ {6} \cdot 5 ^ {3}}{3 \cdot 269 \cdot 107 ^ {9}} = 470\frac{6.890740726224063 \times 10^{20}}{1.4836365844230648 \times 10^{21}} = 470.464449367087$$