Assume that you have a $5,000,000 mortgage with a 4.5% interest rate with monthly payments and a 20-year amortization period and a 5-year term (balloon note). Calculate the outstanding mortgage balance at the end-of-year 5 (month 60).  Round to nearest penny.

To calculate the outstanding mortgage balance at the end of year 5 (after 60 months) for a mortgage with the given parameters, we will first find the monthly payment and then determine the remaining balance at the end of 60 months.

### Step-by-Step Solution

1. **Determine the Monthly Payment**:
   The monthly payment $ M $ for a mortgage can be calculated using the formula:

   \[
   M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}
   \]

   Where:
   - $ P = 5,000,000 $ (the principal amount)
   - $ r = \frac{4.5\%}{12} = \frac{0.045}{12} = 0.00375 $ (monthly interest rate)
   - $ n = 20 \times 12 = 240 $ (total number of payments)

2. **Calculate the Remaining Balance**:
   The outstanding balance after 60 months can be calculated using the formula for the remaining balance of a loan:

   \[
   B = P \left( \frac{(1 + r)^n - (1 + r)^m}{(1 + r)^n - 1} \right)
   \]

   Where:
   - $ B $ is the remaining balance after $ m = 60 $ months.
   - Other variables remain as defined above.

Let's perform the calculations.The outstanding mortgage balance at the end of year 5 (after 60 months) is **$4,134,999.52**.

Would you like to see more details or have any questions?

### Related Questions:
1. How does the interest rate impact the monthly payments and outstanding balance?
2. What would the outstanding balance be if the interest rate was 5% instead of 4.5%?
3. How would the remaining balance change if the amortization period was 30 years instead of 20 years?
4. What is the total interest paid during the first 5 years of this mortgage?
5. How can you calculate the monthly payment for any loan amount, interest rate, and term?

**Tip:** Understanding how the amortization period and interest rate affect loan repayments can help you make more informed decisions about borrowing and refinancing.

Assume that you have a $5,000,000 mortgage with a 4.5% interest rate with monthly payments and a 20-year amortization period and a 5-year term (balloon note). Calculate the outstanding mortgage balance at the end-of-year 5 (month 60). Round to nearest penny.

Learn how to calculate the outstanding mortgage balance at the end of year 5 for a $5,000,000 mortgage with a 4.5% interest rate, monthly payments, a 20-year amortization period, and a 5-year term. This step-by-step guide covers key financial concepts and provides the precise remaining balance rounded to the nearest penny.

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