Question

Maria and John have been married for 2 years and just learned that they are pregnant. They have been renting a small apartment but decide to purchase a house. The one they have found has a selling price of $300,000. They will make a 20% down payment. They are considering 2 financing options at their credit union: Option 1: 3.125% interest 30-year mortgage: Option 2: 2.5% interest 15-year mortgage: Answer the following questions showing all your work to reach each answer. A. Which option will result in a lower monthly payment if they take the full term of the mortgage? What will that monthly payment be? B. Which option will result in the most total interest if they take the full term of the mortgage? What will that total interest be?

Answer 1

Option 1 will result in a lower monthly payment of approximately $1,032.26. Option 1 will result in the most total interest paid of approximately $273,574.40.

Step-by-step explanation:

A. Monthly Payment

To determine the monthly payment for each financing option, we need to calculate the loan amount. The selling price of the house is $300,000 and they will make a 20% down payment, which is $60,000.

Option 1: 3.125% interest 30-year mortgage

The loan amount is $300,000 - $60,000 = $240,000.

Using the loan amount, interest rate, and loan term in the mortgage payment formula, we can calculate the monthly payment:

Monthly Payment = (Loan Amount x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Months))

Monthly Payment = ($240,000 x 0.03125) / (1 - (1 + 0.03125)^(-30x12))

Monthly Payment ≈ $1,032.26

Option 2: 2.5% interest 15-year mortgage

The loan amount is the same, $240,000.

Using the loan amount, interest rate, and loan term in the mortgage payment formula, we can calculate the monthly payment:

Monthly Payment = (Loan Amount x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Months))

Monthly Payment = ($240,000 x 0.025) / (1 - (1 + 0.025)^(-15x12))

Monthly Payment ≈ $1,600.48

Conclusion: Option 1 will result in a lower monthly payment of approximately $1,032.26.

B. Total Interest

To calculate the total interest paid over the full term of each mortgage, we can subtract the loan amount from the total amount paid.

Option 1: Total Interest = (Monthly Payment x Months) - Loan Amount

Total Interest = ($1,032.26 x 30x12) - $240,000

Total Interest ≈ $273,574.40

Option 2: Total Interest = (Monthly Payment x Months) - Loan Amount

Total Interest = ($1,600.48 x 15x12) - $240,000

Total Interest ≈ $88,085.60

Conclusion: Option 1 will result in the most total interest paid of approximately $273,574.40.