The FRED Blog has discussed data from the High-Quality Market (HQM) corporate bond yields release reported by the US Department of the Treasury. In short, that executive agency of the federal government uses the spot rate yields of actual high-quality (that is, low-risk-of-default) corporate bonds to calculate the interest rates of 200 individual bonds with maturity dates extending far into the future. Up to 100 years in the future, in fact.

The FRED graph above shows the calculated interest rate of a hypothetical 100-year bond. The latest data available at the time of this writing is from December 2023: As of that date, the yield of a bond maturing in December 2123, had it been possible then to buy one, was projected to be 5.1%.

This information is used by the Internal Revenue Service (IRS) to calculate the present value of payment from defined benefit plans. The standard formula to compute the present value (PV) of a future value (FV) payment is PV=FV*(1/(1+i)^n), where i is the interest rate and n is the number of periods between now and the future date. The Treasury data provide the value of the interest rates in the IRS’s present value calculations.

So, how are the present values of very distant future payments looking lately? The FRED graph shows that the 100-year interest rate followed a decreasing trend between January 1984 and August 2020. Basic algebra shows that lower values of interest rates, holding constant future values and the number of periods, boost the present value of future payments. The inverse is true when interest rates rise and that has generally been the case during the past three years. Thus, as the present values of very distant future payments decrease, perhaps we should conclude this post by saying carpe diem.

How this graph was created: Search the alphabetical list of FRED releases for “Corporate Bond Yield Curve” and select “Corporate Bond Spot Rates by Maturity, Monthly, Not Seasonally Adjusted.” Scroll all the way down the page to select the series “100-year.”

Suggested by Diego Mendez-Carbajo.

Months of the year differ in terms of economic activity, so it’s often difficult to compare them. Seasonal factors are often at play, such as end-of-year holidays that raise postal employment and retail sales.

Months also have different numbers of workdays, depending on when holidays fall in the week. So it may also be difficult to compare the same month across years. The FRED graph above shows the number of workdays within a month, taken from a Board of Governors release related to the automobile industry: The range spans from 20 to 23 days, a 15% difference. When you compare year-to-year variations on a monthly or even quarterly basis, you may want to consider the number of workdays. And this graph doesn’t even take into account all federal or regional holidays.

One constant source of variation, though, is the month of February. It always has 20 workdays, except for leap years, when an additional day is thrown in. Today, in fact. Thus, this February will be 5% more productive than usual because this additional day is a workday. For the quarter, it will be roughly one-third of that; for the year, it will be one-twelfth. And these are not negligible differences when you think about yearly growth numbers.

How this graph was created: Search FRED for and select “weekdays.”

Suggested by Christian Zimmermann.

The FRED graph above shows the evolution of e-commerce as a proportion of total retail sales. It’s no secret e-commerce has become more prominent and that it boomed during the pandemic, when access to retail premises was restricted. So, what’s the economic lesson here?

First, it’s important to realize that any particular economic activity measured as a share of an aggregate economic activity cannot grow indefinitely in any significant way: It can never go above 100%. Given that, we would expect the share of e-commerce to level off at some point. Has it?

What we do know is that e-commerce is back on its pre-pandemic trend, after a temporary bump in early 2020. Revisit this post in a year or two for a longer view, or add this graph to your FRED dashboard and track it at your leisure.

How this graph was created: Search FRED for “e-commerce” and select the “E-Commerce Retail Sales as a Percent of Total Sales” series.

Suggested by Christian Zimmermann.