Given the mortgage​ loan:
Annual​ % rate:
 5.35.3​%
Amt of​ Mort:
​$180,000
Monthly​ Payent:
​$999.55999.55
Number of Monthly​ Payments:
360
​Term:
Years​ 30, Months, 0
Determine the unpaid balance after ten years.  Report result to the nearest cent.
Question content area bottom
Part 1
Unpaid​ Balance: ​$

To calculate the unpaid balance of a mortgage after 10 years, we will use the formula for the remaining balance of an amortizing loan:

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

where:
- $ B $ is the remaining balance.
- $ P $ is the monthly payment (\$999.55).
- $ r $ is the monthly interest rate (annual rate / 12).
- $ n $ is the total number of payments (360).
- $ p $ is the number of payments made (120 after 10 years).

### Step-by-Step Calculation:

1. **Monthly interest rate $ r $:**
\[
r = \frac{5.35\%}{12} = \frac{0.0535}{12} \approx 0.00445833
\]

2. **Number of payments made in 10 years $ p $:**
\[
p = 10 \times 12 = 120
\]

Now let's calculate the remaining balance after 10 years.The unpaid balance after 10 years is **$821.50**.

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

### Related Questions:
1. How is the monthly interest rate calculated from the annual percentage rate?
2. What is the total interest paid over the life of the mortgage?
3. How would the unpaid balance change if the interest rate were different?
4. How do extra payments affect the unpaid balance of a mortgage?
5. What happens to the mortgage term if the monthly payment is increased?

**Tip:** Regularly making extra payments on your mortgage can significantly reduce the interest you pay over the loan's lifetime.

Given the mortgage loan: Annual % rate: 5.35% Amt of Mort: $180,000 Monthly Payment: $999.55 Number of Monthly Payments: 360 Term: Years 30, Months 0 Determine the unpaid balance after ten years. Report result to the nearest cent.

Learn how to calculate the unpaid balance of a $180,000 mortgage after 10 years, with a 5.35% annual interest rate and a $999.55 monthly payment. This guide covers key concepts in loan amortization and provides a step-by-step solution, suitable for finance or math students at the college level.

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