You want to take out a $232,000 mortgage (home loan). The interest rate on the loan is 5.5%, and the loan is for 30 years. Your monthly payments are $1,317.27. How much will still be owed after making payments for 10 years? Round your answer to the nearest dollar.
Answer:
$

To determine the remaining balance on a mortgage after 10 years of payments, we need to calculate the outstanding principal using the formula for the remaining balance of a loan:

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

Where:
- $ B $ is the remaining balance
- $ P $ is the loan amount (principal)
- $ r $ is the monthly interest rate
- $ n $ is the total number of payments
- $ p $ is the number of payments made

### Step 1: Convert the annual interest rate to a monthly rate
The annual interest rate is 5.5%, so the monthly rate is:

\[
r = \frac{5.5\%}{12} = 0.0045833
\]

### Step 2: Total number of payments and payments made
- Total payments over 30 years: $ n = 30 \times 12 = 360 $
- Payments made in 10 years: $ p = 10 \times 12 = 120 $

### Step 3: Calculate the remaining balance
Plugging these values into the formula gives:

\[
B = 232,000 \left( \frac{(1 + 0.0045833)^{360} - (1 + 0.0045833)^{120}}{(1 + 0.0045833)^{360} - 1} \right)
\]

Calculating this results in:

\[
B \approx 188,311
\]

Thus, the remaining balance on the mortgage after 10 years of payments is approximately:

$188,311


You want to take out a $232,000 mortgage (home loan). The interest rate on the loan is 5.5%, and the loan is for 30 years. Your monthly payments are $1,317.27. How much will still be owed after making payments for 10 years? Round your answer to the nearest dollar.

Find out how to calculate the remaining balance on a 30-year mortgage of $232,000 after 10 years of payments. This problem involves loan amortization, exponential functions, and uses a key formula to determine the outstanding principal. Suitable for students in Grades 11-12.

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