# More on Mortgages

Mortgage interest rates have recently risen, and are currently very volatile. At the time of this writing, PSECU, my credit union, is offering mortgages at 5.125%, much higher than the 3.125% I locked in at, but lower than the peak above 6% I had recently read about in the news. But what does this mean in practice? Well, let’s run some numbers.

Understanding how expensive a house is can be confusing. The total price of a house is a huge number, more money than we normally ever deal with, for most first-time buyers more money than they’ve ever actually had or seen. It can be intimidating.

The more accessible number – the more relevant number for our day-to-day lives – is the monthly payment. The monthly payment includes principal and interest, and also escrow for property taxes and insurance, but let’s focus on the mortgage and interest right now.

The total principal and interest portion of the payment stays constant, but over time more of the payment goes towards principal, due to amortization. For a standard American 30-year fixed rate mortgage, the size of that monthly payment is a linear function of the size of the mortgage and a non-linear function of the interest.

So at my interest rate of 3.125%, a $100,000 mortgage would correspond to a monthly payment of $428. A more realistic $300,000 mortgage would cost three times that per month, or $1285. If you assume $700 or so in insurance and taxes, that comes out to $1985, a very reasonable total amount. If that were a New York City rent, the occupants need to make 40 times that monthly amount per year, or $79,400, to qualify for the apartment, and so in my mind it’d be reasonable for a person or couple who made that much to live in that house.

What about the new rate of 5.125%? The $100,000 mortgage now has a monthly payment of $544. The $300,000 mortgage would then come out to $1633, for an overall monthly payment (including the estimated taxes and other escrow costs) of $2333. By New York City standards, to qualify for that rent a group of tenants would have to make $93,320.

That’s a 17.5% increase in monthly costs, with the estimated monthly escrow payment included. Without including the monthly escrow payment, that’s a 27.1% increase in monthly payments. That means that a $300,000 mortgage at 5.125% would have the same monthly principal and interest payments as a $381,300 house at 3.125%. If you take escrow payment into account, the equivalence is closer to $350,000, which is still substantially more expensive.

This is to say, houses have now become much more expensive for borrowers, who represent the vast majority of middle class home buyers. The numbers on Zillow now mean something very different from what they meant just a few short months ago.

Will this dampen the insane level of real estate demand? Will this lower home prices to accommodate the fact that many home buyers' budgets will naturally have shifted? Theoretically, yes, but it’s unclear whether we’ll notice in this intense a market.

But it’s important to keep this in mind when thinking about houses. The big total price of each house isn’t the only number that matters. The interest rate can also make a huge difference, especially if it is changing rapidly.