To calculate the total cost of the home for mortgage option A, we need to break it down into the following steps:

Step 1: Determine the Loan Amount

The house costs $325,000, and you have $65,000 for a down payment.

$\text{Loan Amount} = \text{Cost of House} - \text{Down Payment}$ $\text{Loan Amount} = 325,000 - 65,000 = 260,000$

Step 2: Mortgage Payment Calculation

Mortgage Option A has a 30-year loan term at an interest rate of 4.5%. We will use the monthly mortgage payment formula:

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

Where:

• $M$ is the monthly payment.
• $P$ is the principal (loan amount).
• $r$ is the monthly interest rate (annual interest rate divided by 12).
• $n$ is the number of payments (loan term in years multiplied by 12).

For Option A:

• $P = 260,000$
• Annual interest rate = 4.5%, so $r = \frac{4.5\%}{12} = \frac{0.045}{12} = 0.00375$
• $n = 30 \times 12 = 360$ payments

Substituting the values into the formula:

$M = \frac{260,000 \times 0.00375 \times (1 + 0.00375)^{360}}{(1 + 0.00375)^{360} - 1}$

Let's calculate the monthly payment first.

Step 3: Calculate the Total Mortgage Payment Over 30 Years

The total cost of the mortgage over 30 years is:

$\text{Total Payments} = M \times 360$

Finally, we will calculate the total cost of the house, which includes the down payment:

$\text{Total Cost of House} = \text{Down Payment} + \text{Total Payments}$

Let me calculate this for you... Given values principal = 260000 # Loan amount annual_interest_rate = 0.045 # 4.5% monthly_interest_rate = annual_interest_rate / 12 # Monthly interest rate loan_term_months = 30 * 12 # 30 years in months

Monthly mortgage payment formula

M = (principal * monthly_interest_rate * (1 + monthly_interest_rate) ** loan_term_months) /
((1 + monthly_interest_rate) ** loan_term_months - 1)

Total payments over 30 years

total_payments = M * loan_term_months

Total cost of the house

down_payment = 65000 total_cost_of_house = down_payment + total_payments

M, total_cost_of_house # Return monthly payment and total cost of houseThe monthly mortgage payment for Option A is approximately $1,317.38.

The total cost of the house, including the down payment and the total mortgage payments over 30 years, is approximately $539,257.45.

Would you like a breakdown of these calculations or have any further questions? Here are some related questions you could explore:

1. How would the total cost of the house change if the interest rate were different (e.g., 5%)?
2. What is the effect of a larger down payment on the overall cost of the house?
3. How does a mortgage with points (like in Option B) affect the total cost compared to a mortgage without points?
4. How can you calculate the interest paid over the life of the loan?
5. What are the differences between a fixed-rate mortgage and an adjustable-rate mortgage?

Tip: To reduce the total cost of the house, consider increasing your down payment or shopping around for better mortgage rates!