Rosalie obtains a 30 year Fixed Rate, Constant Payment Mortgage with monthly payments for $4,500,000 at 4.38%. Her monthly payment is $20,000. What is the balloon payment for this mortgage after 360 payments are made? (e.g. if you get $50,66666, write 50.67)

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:

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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.

Explore how a $4,500,000 mortgage with a 4.38% fixed rate and $20,000 monthly payments leads to a fully amortized loan after 360 payments, resulting in a balloon payment of $0. Detailed calculations on mortgage amortization and loan repayment included.

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