You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $2,474.79 and you have made every payment on time. The original term of the mortgage was 30 ​years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 5.125% ​(APR). How much do you owe on the mortgage​ today?

To determine the outstanding balance on your mortgage, we need to calculate the remaining principal after making monthly payments for four years and eight months.

The mortgage follows the formula for the remaining balance of a fixed-rate mortgage:

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

Where:
- $ P $ is the remaining balance (the amount you owe today),
- $ M $ is the monthly payment (\$2,474.79),
- $ r $ is the monthly interest rate (annual interest rate divided by 12),
- $ n $ is the remaining number of months in the mortgage term.

### Step 1: Calculate the Monthly Interest Rate
The annual interest rate is 5.125%, so the monthly interest rate is:

\[
r = \frac{5.125\%}{12} = \frac{0.05125}{12} \approx 0.004270833
\]

### Step 2: Determine the Number of Months Paid
The mortgage is exactly 4 years and 8 months old. To find how many months of payments have been made:

\[
\text{Months Paid} = 4 \times 12 + 8 = 48 + 8 = 56 \text{ months}
\]

### Step 3: Determine the Number of Months Remaining
The original mortgage term is 30 years (360 months). After making 56 payments, the remaining number of months is:

\[
\text{Remaining Months} = 360 - 56 = 304 \text{ months}
\]

### Step 4: Apply the Remaining Balance Formula
Now, we will apply these values to the formula to calculate the remaining balance. I'll compute that now.The outstanding balance on your mortgage today is approximately **$420,839.58**.

Would you like any more details on this, or do you have any other questions?

Here are 5 related questions you might consider:
1. How would a change in interest rate affect the remaining balance?
2. How can you calculate the total interest paid over the life of a mortgage?
3. What happens to the balance if you make extra payments?
4. How does the loan term (15 years vs. 30 years) impact monthly payments and overall interest?
5. What are the benefits of refinancing at a lower interest rate?

**Tip:** Refinancing to a lower interest rate can reduce your monthly payments and total interest, but consider the refinancing costs before making a decision.

Learn how to calculate the outstanding mortgage balance after four years and eight months of payments. Using a $2,474.79 monthly payment and a 5.125% APR, this guide walks through the step-by-step calculation of the remaining principal. Ideal for students or individuals interested in understanding mortgage amortization and refinancing.

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