You want to buy a $212,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan at 3.65% interest for the rest.

a) How much money in interest will you save if you finance for 15 years instead of 30 years?

$

To determine how much interest you save by financing for 15 years instead of 30 years, let's calculate the interest for both loan periods.

### Step 1: Calculate the loan amount
You plan to pay a 20% down payment, so:

\[
\text{Down payment} = 0.20 \times 212,000 = 42,400
\]

The loan amount is the remaining 80%:

\[
\text{Loan amount} = 212,000 - 42,400 = 169,600
\]

### Step 2: Calculate monthly payment for the 30-year loan
The formula for the monthly mortgage payment is:

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

where:
- $M$ is the monthly payment
- $P$ is the loan amount ($169,600)
- $r$ is the monthly interest rate (3.65% annual interest divided by 12)
- $n$ is the total number of payments (30 years $\times$ 12 months)

For the 30-year loan:
- $r = \frac{3.65}{100} \div 12 = 0.0030417$
- $n = 30 \times 12 = 360$

### Step 3: Calculate the monthly payment for the 15-year loan
For the 15-year loan, the values change slightly:
- $n = 15 \times 12 = 180$

Now, let me compute the monthly payments and total interest for both loans.By financing the home for 15 years instead of 30 years, you will save approximately **$58,811.50** in interest.

Would you like more details or have any further questions? Here are five related questions to consider:

1. What would be your monthly payment for both the 15-year and 30-year loans?
2. How does the total interest compare between different interest rates?
3. How would the savings change if the down payment percentage was increased?
4. How can additional payments affect the total interest paid on a 30-year loan?
5. What is the impact of different loan terms on affordability over time?

**Tip:** A shorter loan term generally results in higher monthly payments but significant savings on interest over the life of the loan.

You want to buy a $212,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan at 3.65% interest for the rest. a) How much money in interest will you save if you finance for 15 years instead of 30 years?

Discover how much interest you can save by financing a $212,000 home over 15 years instead of 30 years at a 3.65% interest rate. Learn the step-by-step breakdown of loan amortization, monthly payments, and total interest saved, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation