The Turners have purchased a house for $180,000. They made an initial down payment of $20,000 and secured a mortgage with interest charged at the rate of 5.5%/year on the unpaid balance. (Interest computations are made at the end of each month.) Assume that the loan is amortized over 30 years. (Round your answers to the nearest cent.)
(a) What monthly payment will the Turners be required to make?
$ 
908.46
 
Correct: Your answer is correct.


(b) What will be their total interest payment?
$ 
167046.46
 
Correct: Your answer is correct.


(c) What will be their equity (disregard depreciation) after 10 years?

To find the equity that the Turners will have after 10 years, we need to calculate the remaining balance on their mortgage after 10 years and then subtract this from the initial loan amount.

Here’s how we approach this step-by-step:

### Step 1: Loan and Payment Details
- Purchase Price of the house: $180,000
- Down payment: $20,000
- Mortgage amount: $180,000 - $20,000 = $160,000
- Interest rate: 5.5% per year compounded monthly = 0.055 / 12 = 0.004583 per month
- Loan term: 30 years = 360 months
- Monthly payment: $908.46 (already given)

### Step 2: Calculate the remaining balance after 10 years
After 10 years, the Turners will have made 120 monthly payments (since 10 years × 12 months = 120 months). To find the remaining balance after 120 payments, we can use the remaining balance formula for a fixed-rate mortgage:

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

Where:
- $ B $ is the remaining balance
- $ P $ is the loan amount ($160,000)
- $ r $ is the monthly interest rate (0.004583)
- $ n $ is the total number of payments (360)
- $ m $ is the number of payments already made (120)

Let's calculate the remaining balance after 10 years.The remaining balance on the mortgage after 10 years is approximately \$132,065.59.

### Step 3: Calculate the equity after 10 years
Equity is the value of the house minus the remaining balance on the mortgage. The house was purchased for \$180,000, and the remaining balance after 10 years is \$132,065.59.

\[
\text{Equity} = \text{House Value} - \text{Remaining Balance} = 180,000 - 132,065.59 = 47,934.41
\]

Therefore, the Turners' equity after 10 years is approximately **\$47,934.41**.

Do you want further details or have any questions?

Here are 5 questions related to this topic:
1. How does the interest rate affect the total mortgage payments?
2. What is the difference between amortization and interest-only mortgages?
3. How can additional payments affect the mortgage term and equity?
4. What are the tax benefits of owning a house with a mortgage?
5. How does home equity affect the ability to refinance a loan?

**Tip**: Making extra payments towards the principal early on in a mortgage can significantly reduce the total interest paid over the life of the loan.

The Turners have purchased a house for $180,000. They made an initial down payment of $20,000 and secured a mortgage with interest charged at the rate of 5.5%/year on the unpaid balance. (Interest computations are made at the end of each month.) Assume that the loan is amortized over 30 years. (Round your answers to the nearest cent.) (a) What monthly payment will the Turners be required to make? (b) What will be their total interest payment? (c) What will be their equity (disregard depreciation) after 10 years?

Learn how to calculate mortgage payments, total interest, and home equity after 10 years on a $180,000 house with a 5.5% interest rate. This detailed guide walks through amortization formulas, remaining balance calculation, and equity determination. Ideal for advanced high school or college students.

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