You are thinking of purchasing a house. The house costs $300,000. You have $ 41,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 35-year mortgage that requires annual payments and has an interest rate of 4.0% per year. What will your annual payment be if you sign up for this mortgage?

The annual payment is $

. (Round to the nearest dollar.)

To calculate the annual payment for the mortgage, we can use the formula for the annuity payment:

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

Where:
- $ P $ is the principal (the amount borrowed).
- $ r $ is the annual interest rate.
- $ n $ is the number of payments (years).

Given:
- The cost of the house: $300,000
- Down payment: $41,000
- Principal (amount to be borrowed): $ 300,000 - 41,000 = 259,000 $
- Interest rate $ r = 4\% = 0.04 $
- Number of payments $ n = 35 $

Let's calculate the annual payment.

\[
\text{Annual Payment} = \frac{259,000 \times 0.04 \times (1 + 0.04)^{35}}{(1 + 0.04)^{35} - 1}
\]

Now, let's compute the value.The annual payment for the mortgage will be **$13,877**.

Would you like any additional details or have any questions? 

Here are some related questions you might find interesting:

1. How much interest will you pay over the entire 35 years?
2. What will be the total cost of the house after the mortgage is paid off?
3. How would your payments change if the interest rate was 5% instead of 4%?
4. What is the impact of making an additional payment each year towards the principal?
5. How would a shorter mortgage term, such as 20 years, affect your annual payment?
6. How does the down payment percentage affect the mortgage payments?
7. What are the benefits of making bi-weekly payments instead of annual payments?
8. How can you refinance a mortgage to reduce payments?

**Tip:** Always consider the total interest paid over the life of a mortgage, as it can significantly impact the overall cost of the house.

Learn how to calculate the annual mortgage payment for a house priced at $300,000 with a down payment of $41,000 and a 35-year mortgage term at 4.0% interest rate. Get the exact annual payment amount with detailed step-by-step calculation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation