Bill and Kim Johnson are purchasing a house for

​$326 comma 000326,000.

Their bank requires them to pay a

2020​%

down payment. The current mortgage rate is

88​%,

and they are required to pay one point at the time of closing. Determine the total amount Bill and Kim will pay for their​ house, including​ principal, interest, down​ payment, and points​ (do not include taxes and​ homeowners' insurance) for the following lengths of their mortgage.With a

2020​-year

​mortgage, Bill and Kim will pay a total of

​$enter your response here

Let's break this down step by step:

### 1. **Down Payment**:
The bank requires Bill and Kim to pay a 20% down payment on the house price.

- House price: $ \$326,000 $
- Down payment: $ 20\% $

\[
\text{Down payment} = 0.20 \times 326,000 = 65,200
\]

### 2. **Loan Amount**:
After the down payment, the remaining amount will be financed through a mortgage.

\[
\text{Loan amount} = 326,000 - 65,200 = 260,800
\]

### 3. **Points**:
One point is 1% of the loan amount, and they are required to pay one point at the time of closing.

- Points to be paid: $ 1\% \times 260,800 = 2,608 $

### 4. **Interest Calculation**:
The mortgage rate is 8% annually, and we will use this to calculate the total interest Bill and Kim will pay over a 20-year mortgage.

We will use the standard formula for calculating monthly mortgage payments:

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

where:
- $ M $ is the monthly mortgage payment,
- $ P $ is the loan amount (\$260,800),
- $ r $ is the monthly interest rate (annual interest rate divided by 12), 
- $ n $ is the number of months in the mortgage (20 years × 12 = 240 months).

\[
r = \frac{8\%}{12} = 0.00667
\]
\[
n = 240 \text{ months}
\]

Let's calculate the monthly payment and the total interest. I'll compute that.### 5. **Monthly Payment**:
The monthly mortgage payment comes out to approximately $ \$2,181.44 $.

### 6. **Total Mortgage Payment**:
Over 20 years, the total amount Bill and Kim will pay on the mortgage is:

\[
\text{Total mortgage payment} = \$523,544.57
\]

### 7. **Total Interest Paid**:
The total interest paid over the 20-year mortgage period is:

\[
\text{Total interest} = \$262,744.57
\]

### 8. **Final Total**:
Now, we can sum up all the payments:

- Down payment: $ \$65,200 $
- Total mortgage payment: $ \$523,544.57 $
- Points: $ \$2,608 $

\[
\text{Total amount paid} = 65,200 + 523,544.57 + 2,608 = 591,352.57
\]

### Conclusion:
Bill and Kim will pay a total of approximately **\$591,352.57** for their house over a 20-year mortgage period, including the principal, interest, down payment, and points.

Would you like more details on any part of this calculation?

### Related Questions:
1. How does changing the down payment percentage affect the overall cost of the mortgage?
2. How would a lower interest rate (e.g., 6%) change the total amount paid?
3. What if they opt for a 15-year mortgage instead of 20 years?
4. How do mortgage points affect the overall cost of a mortgage?
5. What would happen if they increased their monthly payments to pay off the loan faster?

### Tip:
Paying extra on your mortgage can significantly reduce the interest paid over time!

Bill and Kim Johnson are purchasing a house for $326,000. Their bank requires them to pay a 20% down payment. The current mortgage rate is 8%, and they are required to pay one point at the time of closing. Determine the total amount Bill and Kim will pay for their house, including principal, interest, down payment, and points (do not include taxes and homeowners' insurance) for the following lengths of their mortgage: 20 years.

Calculate the total amount Bill and Kim will pay for their $326,000 house, including a 20% down payment, 8% mortgage rate, and one point. This detailed step-by-step guide explains how to compute the down payment, loan amount, points, and total interest over a 20-year mortgage.

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