Present value. You are currently in the job market. Your dream is to eam a six-figure salary \( (\$ 150,000) \). You hope to accomplish this goal within the next 25 years. In your field, salaries grow at \( 4 \% \) per year. What starting salary do you need to reach this goal? What starting salary do you need to reach this goal? \( \$ \square \) (Round to the nearest cent.)

To find the starting salary needed to reach a six-figure salary of $150,000 within 25 years, considering a 4% annual growth rate, we can use the formula for compound interest: \[ A = P \times (1 + r)^n \] Where: - \( A \) is the future value (six-figure salary of $150,000), - \( P \) is the present value (starting salary), - \( r \) is the annual growth rate (4%), - \( n \) is the number of years (25 years). Given that the future value \( A = \$150,000 \), the annual growth rate \( r = 4\% = 0.04 \), and the number of years \( n = 25 \), we can solve for the present value \( P \) (starting salary) using the formula: \[ P = \frac{A}{(1 + r)^n} \] Substitute the given values into the formula to find the starting salary needed to reach the goal of earning a six-figure salary within 25 years. Calculate the value by following steps: - step0: Calculate: \(\frac{150000}{\left(1+0.04\right)^{25}}\) - step1: Add the numbers: \(\frac{150000}{1.04^{25}}\) - step2: Convert the expressions: \(\frac{150000}{\left(\frac{26}{25}\right)^{25}}\) - step3: Simplify the expression: \(\frac{150000}{\frac{26^{25}}{25^{25}}}\) - step4: Rewrite the expression: \(\frac{150000\times 25^{25}}{26^{25}}\) The starting salary needed to reach a six-figure salary of $150,000 within 25 years, considering a 4% annual growth rate, is approximately $56,267.52. Therefore, you would need to start with a salary of $56,267.52 to reach the goal of earning a six-figure salary within 25 years.