Step 1 :Given the amount financed \(P = \$15000\), the annual percentage rate \(r = 5.5\% = 0.055\), the number of payments per year \(n = 12\), and the time in years \(t = 4\).
Step 2 :We first convert the annual interest rate to a monthly interest rate by dividing it by 12. So, \(r_{monthly} = \frac{r_{annual}}{12} = \frac{0.055}{12} = 0.004583333333333333\).
Step 3 :Then, we calculate the total number of payments, which is the number of payments per year times the number of years. So, \(n = 12 \times 4 = 48\).
Step 4 :We substitute these values into the formula for the monthly payment of an installment loan: \(M = P \times \frac{r_{monthly} \times (1 + r_{monthly})^n}{(1 + r_{monthly})^n - 1}\).
Step 5 :Substituting the given values, we get \(M = 15000 \times \frac{0.004583333333333333 \times (1 + 0.004583333333333333)^{48}}{(1 + 0.004583333333333333)^{48} - 1} = 348.84712840864455\).
Step 6 :Rounding to the nearest cent, we get \(M \approx \$348.85\).
Step 7 :So, the monthly payment for the installment loan is approximately \$348.85. Therefore, the final answer is \(\boxed{348.85}\).