The Flemings secured a bank loan of $392,000 to help finance the purchase of a house. The bank charges interest at a rate of 4%/year on the unpaid balance, and interest computations are made at the end of each month. The Flemings have agreed to repay the loan in equal monthly installments over 25 years. What should be the size of each repayment if the loan is to be amortized at the end of the term? (Round your answer to the nearest cent.)

To determine the size of each monthly repayment for the Flemings' loan, we can use the formula for amortizing a loan with equal monthly payments. The general formula is:

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

Where:
- $M$ is the monthly payment,
- $P$ is the loan amount,
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of monthly payments (loan term in years multiplied by 12).

### Given information:
- Loan amount $P = 392,000$,
- Annual interest rate $= 4\%$,
- Loan term $= 25$ years.

### Step-by-step calculation:
1. **Convert the annual interest rate to a monthly interest rate**:
   \[
   r = \frac{4\%}{12} = 0.04 / 12 = 0.0033333
   \]

2. **Calculate the total number of monthly payments**:
   \[
   n = 25 \times 12 = 300
   \]

Now, substituting the values into the formula:

\[
M = \frac{392,000 \times 0.0033333 \times (1 + 0.0033333)^{300}}{(1 + 0.0033333)^{300} - 1}
\]

Let's calculate the monthly payment.The size of each monthly repayment for the Flemings' loan would be **$2,069.12**, rounded to the nearest cent.

Would you like more details on any part of this solution? Here are 5 related questions for further exploration:

1. How does increasing the loan term affect the monthly payment amount?
2. What happens to the monthly payments if the interest rate changes to 5%?
3. How can the total interest paid over the loan term be calculated?
4. What portion of each monthly payment goes toward interest vs. principal in the first month?
5. How much will the Flemings have paid in total over the 25-year term?

**Tip:** Reducing the loan term significantly decreases the total interest paid over time, even if the monthly payments are higher.

Find out how to calculate the monthly repayment amount for a $392,000 home loan with a 4% annual interest rate over 25 years. This problem uses the loan amortization formula and involves concepts in algebra and finance, suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation