After making payments of $909.10 for 4 years on your 30-year loan at 8.9%, you decide to sell your home. What is the loan payoff? 

To find the loan payoff after making payments of $909.10 for 4 years on a 30-year mortgage at 8.9%, we will first break down the process:

### Step 1: Loan Information
- **Loan term**: 30 years
- **Interest rate**: 8.9% (annual)
- **Payments made**: 4 years (or 48 months)
- **Monthly payment**: $909.10

### Step 2: Use the Loan Amortization Formula
The loan amortization formula to calculate the remaining loan balance is:

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

Where:
- $B$ = balance of the loan after payments
- $P$ = original loan amount
- $r$ = monthly interest rate
- $n$ = total number of payments (360 for 30 years)
- $p$ = number of payments already made (48 for 4 years)

### Step 3: Calculate the Original Loan Amount
To determine the original loan amount, use the formula for monthly mortgage payments:

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

Where:
- $M$ is the monthly payment ($909.10),
- $P$ is the original loan amount,
- $r$ is the monthly interest rate ($8.9\% / 12 = 0.0074167$),
- $n$ is the number of payments (360 months).

I'll calculate the original loan amount $P$ and then use it to find the payoff amount after 4 years.

The original loan amount was approximately **$114,002.62**.

After making payments for 4 years, the loan payoff amount (the remaining balance) is approximately **$110,352.96**.

Would you like more details on how this was calculated or have any further questions?

Here are 5 related questions to deepen your understanding:
1. How does the interest rate affect the loan payoff over time?
2. What portion of the monthly payment goes toward interest versus principal in the early years of the loan?
3. How would refinancing the loan at a lower interest rate impact the loan balance?
4. How do extra payments affect the loan payoff amount?
5. What is the difference between a fixed-rate mortgage and an adjustable-rate mortgage?

**Tip**: Making extra payments towards the principal early on in a mortgage can significantly reduce the overall interest paid and the loan term!

After making payments of $909.10 for 4 years on your 30-year loan at 8.9%, you decide to sell your home. What is the loan payoff?

Learn how to calculate the loan payoff after making $909.10 monthly payments for 4 years on a 30-year mortgage at 8.9%. This solution covers key concepts like loan amortization, interest rates, and mortgage payments, suitable for students and homeowners looking to understand financial mathematics.

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