One retailer charges \( \$ 1028 \) for a certain computer. A firm of tax accountants buys 7 of these computers. It makes a down payment of \( \$ 1100 \) and agrees to amortize the balance with monthly payments at \( 15 \% \) interest for 5 years. Prepare an amortization schedule showing the first four monthly payments for this loan. Write the equation that can be used to find the amount of each monthly payment. PMT \( =\frac{\mathrm{PV} \cdot \square}{1-(1+\square)} \) where PV \( =\square \) (Type integers or decimals. Simplify your answers.)

To calculate the monthly payment for the loan, we first need to find the total cost of the computers and determine the balance after the down payment. The total cost for 7 computers is: \[ \text{Total Cost} = 7 \times 1028 = 7196 \] After making a down payment of \( \$1100 \), the remaining balance (PV) will be: \[ \text{PV} = 7196 - 1100 = 6096 \] The amortization will be for 5 years (or 60 months) at an annual interest rate of 15%. The monthly interest rate (r) is therefore: \[ r = \frac{15\%}{12} = 0.0125 \] Now, we can use the formula for the monthly payment (PMT): \[ PMT = \frac{PV \cdot r}{1 - (1 + r)^{-n}} \] where \( n \) is the total number of payments (60 months). Plugging in the values: \[ PMT = \frac{6096 \cdot 0.0125}{1 - (1 + 0.0125)^{-60}} \] Calculating this gives us: \[ PMT \approx \frac{76.2}{1 - (1.0125)^{-60}} \approx \frac{76.2}{0.4693} \approx 162.57 \] Thus, the equation for the monthly payment is: \[ PMT = \frac{6096 \cdot 0.0125}{1 - (1 + 0.0125)^{-60}} \] Now let's summarize the first four monthly payments using this payment figure. 1. **Payment 1:** - Interest for the first month: \( 6096 \times 0.0125 = 76.20 \) - Principal repayment: \( 162.57 - 76.20 = 86.37 \) - Remaining balance: \( 6096 - 86.37 = 6009.63 \) 2. **Payment 2:** - Interest: \( 6009.63 \times 0.0125 \approx 75.12 \) - Principal repayment: \( 162.57 - 75.12 \approx 87.45 \) - Remaining balance: \( 6009.63 - 87.45 \approx 5922.18 \) 3. **Payment 3:** - Interest: \( 5922.18 \times 0.0125 \approx 74.02 \) - Principal repayment: \( 162.57 - 74.02 \approx 88.55 \) - Remaining balance: \( 5922.18 - 88.55 \approx 5833.63 \) 4. **Payment 4:** - Interest: \( 5833.63 \times 0.0125 \approx 72.92 \) - Principal repayment: \( 162.57 - 72.92 \approx 89.65 \) - Remaining balance: \( 5833.63 - 89.65 \approx 5743.98 \) To summarize the first four payments: - Payment 1: \( 162.57 \) - Payment 2: \( 162.57 \) - Payment 3: \( 162.57 \) - Payment 4: \( 162.57 \) with remaining balances fluctuating based on the calculations above. So the monthly payment is approximately \( 162.57 \). Happy amortizing!