The effective interest rate

If I have three different loans at three different interest rates, I can take the total interest I pay during a year and divide it by my total debt to get something called the "effective" interest rate.

My dumb-ass way of doing it is to take the total interest cost for one year, and divide it by the total debt I owe in the same year. Because it's easy to do at FRED, and I never thought twice about it.

But after making a lot of graphs showing debt, I know that debt totals are given as "end of period" data -- typically, the end of the year, or the end of the quarter. And thinking about it, it doesn't seem right to divide this year's interest cost by the amount of debt I will owe at the end of this year. I pay interest on what I owe, not on what I'm gonna owe.

The interest I owe this year is based on the debt I owe since the start of this year (or the end of the year before). I should divide this year's interest by the debt I owed at the end of last year. Thinking about it, I think that's right.

I should say, though, that I didn't think of it on my own. I read about it recently in an old PDF, the Fisher Dynamics PDF by Mason and Jayadev. On page 10 they write:

the effective interest rate [is] computed as the ratio of total interest payments to the stock of debt

 and on the following page:

The effective interest rate i is total interest payments divided by the stock of debt at the beginning of the period.

Or, since debt is measured as "end of period" totals, the effective interest rate is "interest paid" as a percent of "debt outstanding at the end of the year before."

But at least, now that I thought it through in my own way, I should be able to remember it. And since what I'm thinkin does correspond to the Mason and Jayadev calculation, I think I have it right.

Now what I want to know is: Does it make a difference? So I'm off by a year, so what?

I got the data for household debt from FRED, which is actually liabilities of "households and nonprofit organizations". Then I got the interest paid data for households and nonprofits. Then I moved the data to Excel:

Dividing this year's interest cost by last year's debt number gives a consistently higher effective interest rate than you get with the "same year" calculation. Yes, it makes a difference.

The orange line being higher means that I'm dividing by a smaller number: by a consistently smaller number. In other words, last year's debt number is consistently smaller than this year's debt number.

Yeah that's true. Our debt is growing all the time.

So the effective interest rate is higher than my "same year" calculation says, because debt is growing. This conclusion is confirmed by the graph since 2008, when the growth of debt suddenly slowed: The gap between the lines closes.