What is the effect of interest rates and home prices on affordability?

Introduction

With rising interest rates and home prices exerting pressure on the housing market, today's market (February 2024) homes are more unaffordable than ever. As a potential homebuyer, I am looking for a tool that can show how changes in interest rates and home prices affect the affordability of a home, as measured by the estimated monthly payment.

Assumptions

To estimate how affordable a home is, I use a formula that calculates the monthly mortgage payment. This formula considers the loan's principal amount, monthly interest rate, and total payments over the loan's term. The formula looks like this:

Monthly Payment=(P×r) / (1−(1+r)^-n​)

Where:

• P represents the loan amount

• r is the monthly interest rate, and

• n is the total number of payments.

My Assumptions and Variables:

• Home Price (h): This is the total price of the home I'm considering.

• Down Payment Percentage (20%): This is the portion of the home's price that I plan to pay upfront, which reduces the loan amount.

• Loan Term (30 years): This is how long I have to pay back the loan.

• Annual Interest Rate (i): This is the yearly rate the lender charges for borrowing the money.

From there, I calculate the down payment as 20% of the home price, reducing the loan amount I need. I convert the annual interest rate to a monthly rate by dividing by 12 and converting the loan term into the total monthly payments.

Additional Costs:

To fully understand my monthly housing expenses, I also consider additional costs beyond just the principal and interest of the mortgage:

• Property Tax ($362/month): This is what I allocate monthly for annual property taxes.

• Homeowner's Insurance ($66/month): This is the monthly premium to insure the home.

• PMI ($0/month): Private Mortgage Insurance, which I don't have to pay because my down payment is 20%.

• HOA Fees ($0/month): Homeowners Association fees, which aren't applicable to the home I'm looking at.

I sum up these additional costs to understand the full scope of my monthly housing expenses beyond just the mortgage payment.

Calculating My Monthly Mortgage Payment

I calculate the monthly mortgage payment using the provided formula, which includes the loan amount, monthly interest rate, and number of payments. This payment reflects the mortgage's principal and interest components only.

To get the total monthly cost of owning the home, I add this calculated monthly mortgage payment to the total additional costs. This gives me a comprehensive view of what I would be paying each month under my assumptions.

Results

The graph below displays the findings, illustrating the relationship between varying interest rates and monthly mortgage payments across different home prices.

Most intuitively, the results report that as interest rates rise, so does the monthly payment required for a mortgage. This pattern holds across all home price points, from $450,000 to $700,000. The data clearly shows the direct correlation between interest rates and monthly payments — higher rates mean higher payments.

As we look closer, it is easy to see that even a small change in interest rates can significantly affect the monthly outlay for homes at various price levels. For example, a jump from a 2% to a 4% interest rate doesn't just double the interest component of the payment; it results in a monthly payment that's hundreds of dollars higher.

I term the green shaded area on the graph "The Zone of Affordability." This zone ranges from $2,000 to $2,700, which is the monthly payment I feel comfortable paying on a mortgage each month. Your zone of affordability will vary depending on your financial situation. The zone reveals that at 7% mortgage rates, I can expect to pay $2,700 for a house priced at $450,000, but as interest rates decline to 2%, I can afford to pay $2,500 for a house priced at $700,000. This means that, more so than price, the interest rate is a critical determinant of housing affordability.

As a prospective homebuyer or simply someone interested in the housing market, this graph is a powerful tool. They remind me of the importance of interest rates in the home-buying process and their significant impact on affordability.