Isaiah has a 30 year mortgage loan on his house. The amount that he borrowed is 250,000 and his interest rate is 8.4% compounded monthly. Isaiah will repay the loan with monthly payments over the 30 years. 

Calculate the outstanding loan balance right after the 120th payment.

To calculate the outstanding loan balance after Isaiah has made the 120th payment on his 30-year mortgage, we will use the formula for the balance of a loan after a certain number of payments have been made.

### Key Parameters:

- **Loan amount (P)**: \$250,000
- **Annual interest rate (r)**: 8.4%
- **Compounded monthly**, so the **monthly interest rate** $i = \frac{8.4\%}{12} = \frac{0.084}{12} = 0.007$ per month.
- **Number of payments per year**: 12
- **Total number of payments (N)**: 30 years × 12 months/year = 360 payments
- **Number of payments already made**: 120 payments

### Step 1: Monthly Payment Calculation
The formula to calculate the monthly payment is:

\[
M = P \cdot \frac{i(1 + i)^N}{(1 + i)^N - 1}
\]

Where:
- $M$ is the monthly payment,
- $P$ is the loan amount,
- $i$ is the monthly interest rate,
- $N$ is the total number of payments.

### Step 2: Outstanding Balance After 120 Payments
Once we have the monthly payment, we calculate the outstanding balance after 120 payments using the formula:

\[
B_n = P \cdot \frac{(1 + i)^N - (1 + i)^n}{(1 + i)^N - 1}
\]

Where:
- $B_n$ is the remaining balance after $n$ payments,
- $n$ is the number of payments made (120 in this case),
- $i$, $P$, and $N$ are as defined before.

Let’s calculate this step-by-step. I'll first compute the monthly payment and then the outstanding balance after 120 payments.### Results:

1. Isaiah's **monthly payment** is approximately \$1,904.59.
2. The **outstanding loan balance** after making 120 payments is approximately \$221,077.68.

Would you like further details on how these calculations were done or have any questions?

Here are some related questions that you might find interesting:

1. How does the balance change if the interest rate was different?
2. How much total interest would Isaiah pay over the entire loan term?
3. What would the balance be after 15 years of payments?
4. How does making an extra payment each year affect the balance?
5. How much would Isaiah save if the interest rate were 1% lower?

**Tip**: Making extra payments on a mortgage early can significantly reduce the total interest paid over the loan term!

Isaiah has a 30 year mortgage loan on his house. The amount that he borrowed is 250,000 and his interest rate is 8.4% compounded monthly. Isaiah will repay the loan with monthly payments over the 30 years. Calculate the outstanding loan balance right after the 120th payment.

Learn how to calculate the outstanding mortgage loan balance after making 120 payments on a $250,000 loan with an interest rate of 8.4%, compounded monthly. This problem covers loan amortization concepts, key formulas for monthly payments and remaining balance, and is suitable for advanced high school or college students.

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