Sure! Let’s solve for the annual rate of return in 2 steps. --- **Step 1: Write the Future Value of an Ordinary Annuity Formula** The formula for the future value (FV) of an ordinary annuity is: \[ FV = PMT \times \frac{(1 + r)^n - 1}{r} \] Where: - \(FV = \$2,132,822.76\) - \(PMT = \$10,000\) - \(n = 35\) - \(r =\) annual rate of return (unknown) --- **Step 2: Solve for \(r\) (annual rate of return)** Plug in the numbers: \[ 2,132,822.76 = 10,000 \times \frac{(1 + r)^{35} - 1}{r} \] Divide both sides by 10,000: \[ 213.282276 = \frac{(1 + r)^{35} - 1}{r} \] Multiply both sides by \(r\): \[ 213.282276 \cdot r = (1 + r)^{35} - 1 \] \[ (1 + r)^{35} - 213.282276 \cdot r - 1 = 0 \] This equation must be solved for \(r\). Let's estimate \(r\) using trial and error or a financial calculator. Trying \(r = 0.10\) (10%): \[ (1.10)^{35} = 28.102 \] \[ \frac{28.102 - 1}{0.1} = \frac{27.102}{0.1} = 271.02 \] This is higher than 213.28. Trying \(r = 0.08\) (8%): \[ (1.08)^{35} = 14.785 \] \[ \frac{14.785 - 1}{0.08} = \frac{13.785}{0.08} = 172.31 \] This is lower than 213.28. Try \(r = 0.09\) (9%): \[ (1.09)^{35} = 19.848 \] \[ \frac{19.848 - 1}{0.09} = \frac{18.848}{0.09} = 209.42 \] Very close! Try \(r = 0.092\) (9.2%): \[ (1.092)^{35} \approx 21.302 \] \[ \frac{21.302 - 1}{0.092} = \frac{20.302}{0.092} \approx 220.67 \] A bit high. Interpolate between 9.0% (209.42) and 9.2% (220.67): \[ r \approx 9.0\% + \frac{213.28 - 209.42}{220.67 - 209.42} \times 0.2\% \] \[ r \approx 9.0\% + \frac{3.86}{11.25} \times 0.2\% = 9.0\% + 0.069\% = 9.07\% \] --- **Final Answer:** **The annual rate of return is approximately 9.07%.** --- **Explanation:** - **Step 1:** We set up the standard annuity future value formula with your numbers. - **Step 2:** We solved for the unknown rate using algebra and estimation, showing our calculations each step. **Final Answer:** **9.07% annual rate of return.**