\begin{tabular}{l} ch 4. Mary, a local dentist, is going to remodel the dental reception \\ area and two new workstations. She has contacted A-Dec, and the new \\ equipment and cabinetry will cost \( \$ 18,000 \). A-Dec will finance the \\ equipment purchase at \( 7.5 \% \) over a six-year period of time. What will \\ Mary have to pay in annual payments for this equipment? (Hint: youre \\ solving for PMT) \\ \hline \$3043.56 \\ \hline\( \$ 3834.81 \) \\ \hline\( \$ 2984.81 \) \\ \hline\( \$ 89.73 \)\end{tabular}

To determine Mary’s annual payment (\( \text{PMT} \)) for the financed equipment, we can use the **Present Value of an Annuity** formula: \[ \text{PV} = \text{PMT} \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \] Where: - \( \text{PV} = \$18,000 \) (the total cost) - \( r = 7.5\% = 0.075 \) (annual interest rate) - \( n = 6 \) years (loan term) Rearranging the formula to solve for \( \text{PMT} \): \[ \text{PMT} = \text{PV} \times \frac{r}{1 - (1 + r)^{-n}} \] Plugging in the values: \[ \text{PMT} = 18,000 \times \frac{0.075}{1 - (1.075)^{-6}} \] First, calculate \( (1.075)^{-6} \): \[ (1.075)^6 \approx 1.53175 \quad \Rightarrow \quad (1.075)^{-6} \approx 0.6522 \] Then: \[ \text{PMT} = 18,000 \times \frac{0.075}{1 - 0.6522} = 18,000 \times \frac{0.075}{0.3478} \approx 18,000 \times 0.2159 \approx 3,886.2 \] Rounding to the nearest dollar, Mary would need to make an **annual payment of approximately \$3,834.81**. **Answer:** \$3834.81