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$100.000 \times \frac{1}{(1+.06)^{20}}$

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Factor quadratics: special cases

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Q.

100.000 \times \frac{1}{(1+.06)^{20}}

Set up expression: Understand the problem and set up the expression. $\newline$ We need to calculate the value of $100,000$ multiplied by the reciprocal of $(1 + 0.06)$ raised to the power of $20$ . This is a present value calculation in finance, often used to determine the present value of a future sum of money. $\newline$ Expression: $100,000 \times \frac{1}{(1 + 0.06)^{20}}$
Simplify inside parentheses: Simplify the expression inside the parentheses. $\newline$ Calculate the value inside the parentheses, which is $1 + 0.06$ . $\newline$ $1 + 0.06 = 1.06$ $\newline$ Now the expression is $100,000 \times \frac{1}{1.06^{20}}$
Calculate denominator: Calculate the denominator, which is $1.06$ raised to the power of $20$ . Using a calculator, we find that $1.06^{20} \approx 3.207135472$ . Now the expression is $100,000 \times \frac{1}{3.207135472}$
Divide for multiplier: Divide $1$ by the value obtained in Step $3$ . $\newline$ Divide $1$ by $3.207135472$ to get the multiplier for $100,000$ . $\newline$ $1 / 3.207135472 \approx 0.311804782$
Multiply for final answer: Multiply $100,000$ by the value obtained in Step $4$ . $\newline$ Multiply $100,000$ by $0.311804782$ to get the final answer. $\newline$ $100,000 \times 0.311804782 \approx 31,180.4782$

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