Suppose you want to buy a $148,000 home. You found a bank that offers a 30-year loan at 3.9% APR.

What will be your monthly payment? (Round to the nearest cent.)

$

How much would you end up paying the bank for the home after 30 years? (Round to the nearest cent.)

$

Suppose you wanted to reduce the time of your loan to 25 years. What would be your new monthly payment? (Round to the nearest cent.)

$

How much would you end up paying the bank for the home after 25 years? (Round to the nearest cent.)

$

How much did you save by reducing the time of your mortgage loan? (Round to the nearest cent.)


This problem involves calculating the monthly payment and total payment on a fixed-rate mortgage loan. We will use the following formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $ M $ = Monthly payment
- $ P $ = Principal loan amount (in this case, $148,000)
- $ r $ = Monthly interest rate (annual interest rate divided by 12)
- $ n $ = Total number of payments (loan term in years multiplied by 12)

### 1. **Monthly payment for a 30-year loan at 3.9% APR**:

- $ P = 148,000 $
- $ r = \frac{3.9\%}{12} = 0.00325 $ (monthly interest rate)
- $ n = 30 \times 12 = 360 $ (total payments for 30 years)

Let’s calculate the monthly payment.

### 2. **Total amount paid after 30 years**:
This is calculated by multiplying the monthly payment by the total number of payments over the loan period:

\[
\text{Total payment} = M \times n
\]

### 3. **Monthly payment for a 25-year loan at 3.9% APR**:

- $ n = 25 \times 12 = 300 $ (total payments for 25 years)

Let’s calculate the new monthly payment.

### 4. **Total amount paid after 25 years**:

\[
\text{Total payment} = M_{\text{new}} \times 300
\]

### 5. **Savings by reducing the loan period**:
This is the difference between the total amount paid over 30 years and the total amount paid over 25 years.

Now let's calculate all the required values.Here are the results:

1. **Monthly payment for a 30-year loan at 3.9% APR**: 
   \[
   M = \$698.07
   \]

2. **Total amount paid to the bank after 30 years**: 
   \[
   \$251,304.82
   \]

3. **Monthly payment for a 25-year loan at 3.9% APR**: 
   \[
   M = \$773.05
   \]

4. **Total amount paid to the bank after 25 years**: 
   \[
   \$231,914.95
   \]

5. **Savings by reducing the loan period**: 
   \[
   \$19,389.87
   \]

If you have any questions or need further clarification, feel free to ask! Here are 5 follow-up questions:

1. How does the monthly interest rate affect the monthly payment?
2. What would happen if the APR were increased to 4.5% for the same loan?
3. How is the total interest paid over the life of the loan calculated?
4. Would making additional payments affect the savings by reducing the loan period?
5. Can adjusting the loan term (increasing or decreasing) affect the overall affordability?

**Tip:** Paying down the loan principal faster (by either shortening the term or making extra payments) saves a significant amount on interest!

Suppose you want to buy a $148,000 home. You found a bank that offers a 30-year loan at 3.9% APR.

What will be your monthly payment? (Round to the nearest cent.)

How much would you end up paying the bank for the home after 30 years? (Round to the nearest cent.)

Suppose you wanted to reduce the time of your loan to 25 years. What would be your new monthly payment? (Round to the nearest cent.)

How much would you end up paying the bank for the home after 25 years? (Round to the nearest cent.)

How much did you save by reducing the time of your mortgage loan?

Learn how to calculate the monthly payment for a $148,000 home loan at 3.9% APR over 30 years. Discover the total payment to the bank and the savings when reducing the loan term to 25 years. Suitable for Grades 10-12, covering key algebraic and financial concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation