Martha is buying a house that sells for ​$97000. The bank is requiring a minimum down payment of 20​%. To obtain a 35​-year mortgage at 8.0​% ​interest, she must pay 4 points at the time of closing. ​a) Determine the required down payment. ​b) Determine the amount of the mortgage on the property with the 20​% down payment. ​c) Find the cost of 4 points on the mortgage.

Let's break down the problem step by step:

### Given:
- House price = $97,000
- Down payment percentage = 20%
- Mortgage interest rate = 8.0%
- Mortgage term = 35 years
- Points at closing = 4 points

### a) Determine the required down payment

The down payment is calculated as a percentage of the total house price.

\[
\text{Down Payment} = \text{House Price} \times \text{Down Payment Percentage}
\]

\[
\text{Down Payment} = 97,000 \times 0.20 = 19,400
\]

So, the required down payment is **$19,400**.

### b) Determine the amount of the mortgage on the property with the 20% down payment

The mortgage amount is the difference between the house price and the down payment.

\[
\text{Mortgage Amount} = \text{House Price} - \text{Down Payment}
\]

\[
\text{Mortgage Amount} = 97,000 - 19,400 = 77,600
\]

So, the mortgage amount is **$77,600**.

### c) Find the cost of 4 points on the mortgage

Points are fees paid directly to the lender at closing in exchange for a reduced interest rate. Each point is 1% of the mortgage amount.

\[
\text{Cost of Points} = \text{Mortgage Amount} \times \text{Points Percentage}
\]

\[
\text{Cost of Points} = 77,600 \times 0.04 = 3,104
\]

So, the cost of 4 points on the mortgage is **$3,104**.

### Summary:
- **a) Required down payment:** $19,400
- **b) Amount of the mortgage:** $77,600
- **c) Cost of 4 points:** $3,104

Would you like more details on any part of the calculations?  

Here are some related questions for further exploration:
1. How would the down payment change if it was 25% instead of 20%?
2. What would be the mortgage amount if the house price was $120,000?
3. How does the cost of points change if Martha only pays 2 points?
4. What is the monthly mortgage payment if the mortgage interest rate was 7% instead of 8%?
5. How much total interest would Martha pay over the 35 years?
6. What is the total cost of the house including down payment and points?
7. How does the total cost of the house change if the mortgage term is reduced to 30 years?
8. What are the benefits of paying points at closing?

**Tip:** Paying points at closing can reduce your monthly mortgage payment by lowering the interest rate, but it's important to weigh this against the upfront cost.

Learn how to calculate the required down payment, mortgage amount, and cost of points when buying a house. This problem involves financial mathematics, including percentage calculations and mortgage terms. Suitable for adults looking to understand home financing.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation