 I posted a few months ago how the interest rates on Treasury’s I savings bonds reset. Someone at pickleball asked me to explain further. I looked into it and it’s fairly straightforward: the value of an I-bond bought at a particular time increases by the nominal rate (which is the real interest rate set at the time plus the inflation rate set at the time plus a small factor for the interaction of the two.) These rates are set every 6 months. So for the next months that new amount, which includes the interest earned, increases by the new nominal rate. In short, the value of the investment compounds by an interest rate for a 6-month period, then the interest rate for the next 6-month period, etc. There’s one little wrinkle involving what the Treasury calls the “fixed rate” and I call the “real rate.”

In essence, the I bond, except for that little wrinkle, is not different from investing in a CD, except that the interest rate on the I bond will be typically be higher. Let’s say you buy a \$10,000 6-month CD that carries an annual interest rate of 5%. (This is the highest I could find on line; it’s from an on-line bank called CIT Bank.) At the end of the 6 months, you’ll have \$10,250. Then, when 6 months is up, you use the \$10,200 to buy a 6-month CD that carries an annual interest rate of 4% because, let’s say, interest rates have fallen. At the end of the 6 months you’ll have \$10,250 * 1.02 = \$10,455.

Now back to the I bond. Let’s say you buy a \$10,000 I bond that pays an annual rate of 6.89%. (That’s the current annual rate.) This is made up of 3 components: a real rate of 0.4% (the Treasury calls this a fixed rate) + 2 times the semiannual inflation rate of 3.24% plus the semi-annual inflation rate times the 0.4%. So that’s 0.4% + 2* 3.24% + 0.4% * 3.24% = 0.4% + 6.48% + 0.01296% = 6.89296%. Rounding to two decimal places gives 6.89%. So on a 6-month basis, that’s 3.45%. You hold this bond for 6 months and so at the end you have \$10,000 * 1.0345 = \$10,345. See this link for how the Treasury explains it. Notice, by the way, that if the Treasury’s explanation is correct, the Treasury made a little mistake. That third term above should be annual, just like the others. So it should be 0.4% * 6.48%. It doesn’t matter much, though. Done on an annual basis, that third factor would be 0.02592%. So, the total would be 0.4% + 6.48% + 0.02592% = 6.9052%. Rounding to two decimals places, it would be 6.91%, not 6.89%.

Then you decide not to cash the bond but to let it ride and keep collecting interest. Meanwhile the 6-month inflation factor has fallen, say, to 3.00%. One thing hasn’t changed, though. Because you bought when the real rate was 0.4%, you get that 0.4% forever, no matter what happens when the Treasury resets the real rate on bonds bought in the new 6-month period. This is probably why the Treasury calls it a fixed rate rather than my preferred terminology of a real rate. So you get an annual rate of 0.4% + 2*3.00% + 0.4% * 3.00% = 0.4% + 6.00% + 0.012% = 6.52%. At the end of this 6-month period, your investment is worth \$10,345 * 1.0326 = \$10,682.25.

Note: The picture above is of Irving Fisher, one of the greatest U.S. economists of the late 19th and early 20th centuries. He pointed out that interest rates adjust for expected inflation. Indeed we now call the 2nd and 3rd terms in the computations above the “Fisher effect.”