Evaluate ((1-1÷((1+0.08÷52)^(8*52)))÷0.08)÷52

$(1 - 1 \div {(1 + 0.08 \div 52)}^{8 \cdot 52}) \div 0.08 \div 52$

Step 1

Rewrite the division as a fraction.

$\frac{(1 - 1 \div {(1 + 0.08 \div 52)}^{8 \cdot 52}) \div 0.08}{52}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$(1 - 1 \div {(1 + 0.08 \div 52)}^{8 \cdot 52}) \div 0.08 \cdot \frac{1}{52}$

Step 3

Rewrite the division as a fraction.

$\frac{1 - 1 \div {(1 + 0.08 \div 52)}^{8 \cdot 52}}{0.08} \cdot \frac{1}{52}$

Step 4

Simplify the denominator.

Divide $0.08$ by $52$ .

$\frac{1 - 1 \div {(1 + 0.00153846)}^{8 \cdot 52}}{0.08} \cdot \frac{1}{52}$

Add $1$ and $0.00153846$ .

$\frac{1 - 1 \div {1.00153846}^{8 \cdot 52}}{0.08} \cdot \frac{1}{52}$

Multiply $8$ by $52$ .

$\frac{1 - 1 \div {1.00153846}^{416}}{0.08} \cdot \frac{1}{52}$

Raise $1.00153846$ to the power of $416$ .

$\frac{1 - 1 \div 1.89554841}{0.08} \cdot \frac{1}{52}$

Step 5

Simplify the numerator.

Divide $1$ by $1.89554841$ .

$\frac{1 - 1 \cdot 0.52755181}{0.08} \cdot \frac{1}{52}$

Multiply $- 1$ by $0.52755181$ .

$\frac{1 - 0.52755181}{0.08} \cdot \frac{1}{52}$

Subtract $0.52755181$ from $1$ .

$\frac{0.47244818}{0.08} \cdot \frac{1}{52}$

Step 6

Combine fractions.

Divide $0.47244818$ by $0.08$ .

$5.90560235 (\frac{1}{52})$

Combine $5.90560235$ and $\frac{1}{52}$ .

$\frac{5.90560235}{52}$

Divide $5.90560235$ by $52$ .

$0.11356927$