The Turners have purchased a house for $140,000. 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?
$ 


To solve this mortgage-related problem, we'll use the following approach:

### Given Information:
- Purchase price of the house: $140,000
- Down payment: $20,000
- Loan amount (principal): $ 140,000 - 20,000 = 120,000 $
- Annual interest rate: 5.5%
- Loan term: 30 years
- Monthly interest rate: $ \frac{5.5\%}{12} = \frac{0.055}{12} $
- Loan is amortized over 30 years, which is $ 30 \times 12 = 360 $ monthly payments.

### (a) Monthly Payment Calculation

We will use the amortization formula for calculating the monthly payment, $ M $:

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

where:
- $ P $ is the loan amount (principal), $ P = 120,000 $
- $ r $ is the monthly interest rate, $ r = \frac{0.055}{12} $
- $ n $ is the total number of payments, $ n = 360 $

### (b) Total Interest Payment

The total interest paid over the life of the loan is:

\[
\text{Total Interest} = (\text{Monthly Payment} \times n) - P
\]

### (c) Equity after 10 Years

To find the equity after 10 years, we need to calculate the remaining balance after 120 months (10 years). The equity is:

\[
\text{Equity} = \text{House Value} - \text{Remaining Balance}
\]

Let's calculate each part.Here are the results based on the calculations:

### (a) Monthly Payment:
The Turners will be required to make a monthly payment of **$681.35**.

### (b) Total Interest Payment:
The total interest paid over the life of the loan will be **$125,284.85**.

### (c) Equity after 10 Years:
After 10 years, their equity in the house will be **$40,950.81**.

Would you like further details or explanations on any part? Here are some related questions for deeper exploration:

1. How would the monthly payment change if the interest rate was 6%?
2. What if the loan term was 20 years instead of 30 years?
3. How does a higher down payment affect the total interest paid?
4. What is the remaining loan balance after 15 years?
5. How can early payments (like extra monthly contributions) reduce the total interest?

**Tip:** By making even small additional payments on your mortgage principal, you can significantly reduce the interest paid over the life of the loan.

The Turners have purchased a house for $140,000. 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 the monthly payment, total interest, and equity for a $140,000 mortgage at a 5.5% annual interest rate over 30 years. This problem involves key concepts like loan amortization, interest calculations, and equity analysis. Suitable for advanced high school and college-level students.

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