Solve 1-(1+8%/12)^-7

$$1 - ( 1 + \frac { 8 \% } { 12 } ) ^ { - 7 }$$

Evaluate

$$\frac{81346899848551}{1789940649848551}\approx 0.045446702$$

Solution Steps

Express \frac{\frac{8}{100}}{12} as a single fraction.

$$1-\left(1+\frac{8}{100\times 12}\right)^{-7}$$

Multiply 100 and 12 to get 1200.

$$1-\left(1+\frac{8}{1200}\right)^{-7}$$

Reduce the fraction \frac{8}{1200} to lowest terms by extracting and canceling out 8.

$$1-\left(1+\frac{1}{150}\right)^{-7}$$

Add 1 and \frac{1}{150} to get \frac{151}{150}.

$$1-\left(\frac{151}{150}\right)^{-7}$$

Calculate \frac{151}{150} to the power of -7 and get \frac{1708593750000000}{1789940649848551}.

$$1-\frac{1708593750000000}{1789940649848551}$$

Subtract \frac{1708593750000000}{1789940649848551} from 1 to get \frac{81346899848551}{1789940649848551}.

$$\frac{81346899848551}{1789940649848551}$$

Factor

$$\frac{29 \cdot 757457 \cdot 3703267}{151 ^ {7}} = 0.045446702300120316$$