Evaluate 100000/((1-(1+0.02)^-5)/0.02)

$\frac{100000}{\frac{1 - {(1 + 0.02)}^{- 5}}{0.02}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$100000 \frac{0.02}{1 - {(1 + 0.02)}^{- 5}}$

Step 2

Simplify the denominator.

Add $1$ and $0.02$ .

$100000 \frac{0.02}{1 - {1.02}^{- 5}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$100000 \frac{0.02}{1 - \frac{1}{{1.02}^{5}}}$

Raise $1.02$ to the power of $5$ .

$100000 \frac{0.02}{1 - \frac{1}{1.1040808}}$

Divide $1$ by $1.1040808$ .

$100000 \frac{0.02}{1 - 1 \cdot 0.9057308}$

Multiply $- 1$ by $0.9057308$ .

$100000 \frac{0.02}{1 - 0.9057308}$

Subtract $0.9057308$ from $1$ .

$100000 (\frac{0.02}{0.09426919})$

Step 3

Simplify the expression.

Divide $0.02$ by $0.09426919$ .

$100000 \cdot 0.21215839$

Multiply $100000$ by $0.21215839$ .

$21215.83941043$