Erin took out a 15 -year mortgage with an annual interest rate of $48 \%$ to purchase a house for $\$ 320,000$ with a down payment of $\$ 20,000$. Find the amount of the monthly payment needed to amortize this loan The amount of the monthly payment needed to amortize this loan is $\$$ (Round to the nearest cent as needed)

Step 1 ：\(\text{Loan amount} = \text{Total cost of the house} - \text{Down payment}\)

Step 2 ：\(\text{Loan amount} = \$320,000 - \$20,000 = \$300,000\)

Step 3 ：\(\text{Monthly interest rate} = \frac{\text{Annual interest rate}}{12}\)

Step 4 ：\(\text{Monthly interest rate} = \frac{48\%}{12} = 4\%\)

Step 5 ：\(\text{Monthly interest rate} = \frac{4\%}{100} = 0.04\)

Step 6 ：\(P = \frac{r*PV}{1 - (1 + r)^{-n}}\)

Step 7 ：\(P = \frac{0.04 * \$300,000}{1 - (1 + 0.04)^{-180}}\)

Step 8 ：\(P = \frac{\$12,000}{1 - (1.04)^{-180}}\)

Step 9 ：\(P = \frac{\$12,000}{1 - 0.0184}\)

Step 10 ：\(P = \frac{\$12,000}{0.9816}\)

Step 11 ：\(\boxed{P = \$12,224.49}\)