To find the balloon payment after 360 monthly payments on a fixed-rate, constant payment mortgage, we need to determine if there is any remaining balance after the final payment. However, in a fully amortizing mortgage, the balloon payment after 360 payments would be $0, because the loan is paid off completely by then. Let's break down the details of this mortgage:

Key Information:

• Loan amount (P): $4,500,000
• Annual interest rate (r): 4.38% (0.0438)
• Monthly interest rate (r/12): $\frac{4.38\%}{12} = \frac{0.0438}{12} \approx 0.00365$
• Number of payments (n): 360 (30 years × 12 months/year)
• Monthly payment (M): $20,000

Calculation of the remaining balance:

In a fully amortized mortgage, after making all payments (360 months), the remaining balance is expected to be $0 unless there is some miscalculation. Here's why:

1. The monthly payment is designed to cover both the interest and the principal.
2. Since Rosalie is making the required 360 payments of $20,000 each, the loan is structured to ensure the entire $4,500,000 is paid off, including the interest over time.

Balloon Payment:

• After 360 payments, the remaining balance is $0, since this is a fully amortizing loan.
• Therefore, the balloon payment is:

$\boxed{0.00}$

Would you like further details on the calculation? Here are 5 questions related to this topic:

1. How is the monthly payment calculated in a fixed-rate mortgage?
2. What happens if extra payments are made during the mortgage term?
3. What is the difference between fully amortizing loans and balloon payment loans?
4. How does the interest rate affect the monthly payment on a mortgage?
5. What are the tax implications of paying interest on a mortgage?

Tip: In a fixed-rate mortgage, the earlier payments contribute more toward interest, while the later payments pay off more principal.