Hunan bought a car priced at $\$ 15,600$ for $15 \%$ down and equal monthly payments for five years. If interest is $8 \%$ compounded monthly, what is the size of the monthly payment? The monthly payment is $\$ \square$. (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：Hunan bought a car priced at \$15,600. The down payment is 15\% of the total price, which is \$15,600 \times 0.15 = \$2,340.

Step 2 ：The amount that needs to be financed is the total price minus the down payment, which is \$15,600 - \$2,340 = \$13,260. This is the principal for our loan.

Step 3 ：The annual interest rate is 8\%, but it is compounded monthly, so the monthly interest rate is 0.08 ÷ 12 = 0.006666666666666667.

Step 4 ：The loan is for 5 years, so the total number of payments is 5 \times 12 = 60.

Step 5 ：We can then use the formula for the monthly payment on a loan, which is: P = [r*PV] / [1 - (1 + r)^-n], where P is the monthly payment, r is the monthly interest rate, PV is the present value or principal of the loan, and n is the number of payments.

Step 6 ：Substituting the values into the formula, we get: P = [0.006666666666666667 * 13260] / [1 - (1 + 0.006666666666666667)^-60] = 268.8649882643677.

Step 7 ：Rounding to the nearest cent, the monthly payment is \(\boxed{\$268.86}\).