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.”
READER COMMENTS
robc
Apr 6 2023 at 10:18am
I may be out of date, but hasn’t the “fixed rate” for new I-Bonds been set at 0 for a few years now?
David Henderson
Apr 6 2023 at 10:43am
It’s current 0.4%. Check this link.
robc
Apr 6 2023 at 1:19pm
Thanks, I was out of date. I looked it up, from May 2020 thru Oct 2022, I Bonds issued had a 0% fixed rate. So not that out of date.
robc
Apr 6 2023 at 1:25pm
Apparently it was also 0% back in 2013, here is a forum post discussing how the fixed rate portion is determined.
https://www.bogleheads.org/forum/viewtopic.php?t=117959
vince
Apr 6 2023 at 2:39pm
Did the Treasury make a mistake, or is it confusing interest rate terminology and the distinction between nominal and effective interest rates?
If the 6 month inflation rate was .0324, the fixed rate was .004/2, and compounding was semiannual, $1 should convert at year end to 1.0324^2 * 1.002^2 = 1.07012. The Treasury announced an annual rate of .0689296. With semiannual compounding, at year end that would amount to (1+.0689296/2)^2 = 1.07012.
Gail Edwards
Apr 7 2023 at 3:06am
In the second half of the ibond calculations, you multiplied your $10,345 by an entire year of interest 6.52% instead of half 3.26% of that for the six month period you are showing as a final dollar amount. It should be about $10,682 after one year in ibonds.
Richard Ebeling
Apr 7 2023 at 8:06am
Let us remember one other distinction between a CD in a private bank vs. the government bond:
The private bank (in principle) is paying interest from having lent what you have left on deposit to a willing private borrower, who pays back the loan with his own money.
On the government bond, you are being paid back with “other people’s money,” which has been taken by coerced taxes.
A minor point, perhaps, but one worth mentioning.
David Henderson
Apr 7 2023 at 10:34am
Good point, and not necessarily minor.
vince
Apr 7 2023 at 12:32pm
That raises the whole endogenous money question …
MB Walker
Apr 7 2023 at 12:01pm
One more significant difference between I-Bonds and CDs: I-Bonds are exempt from state and local taxes, CDs are not.
David Enna
Apr 7 2023 at 12:09pm
OK, no. 1, the Treasury does not make mistakes in calculating the I Bond’s interest rate. Imagine the uproar if that happened. When the variable rate is calculated after the six months period, the inflation rate is rounded to two decimal points and then doubled to create the new variable rate. The fixed rate is then applied to the variable rate to create the six-month composite rate, with this formula:
Fixed rate
0.40%
Semiannual (1/2 year) inflation rate
3.24%
Composite rate formula: [Fixed rate + (2 x semiannual inflation rate) + (fixed rate x semiannual inflation rate)]
[0.0040 + (2 x 0.0324) + (0.0040 x 0.0324)]
Gives a composite rate of
[0.0040 + 0.0648 + 0.0001296]
Adding the parts gives
0.0689296
Rounding gives
0.0689
Turning the decimal number to a percentage gives a composite rate of
6.89%
Then, how is interest actually earned and compounded. It’s a bit wacky, probably dating back to the time when people bought $25 savings bonds with each paycheck. This description is from the Bogleheads wiki, and it is the best I’ve seen:
All bond values are based on the $25 bond. A $5000 bond is worth 200 times what a $25 bond is worth; a $100 bond is worth 4 times what a $25 bond is worth. If you have a $80 electronic bond at TreasuryDirect, it is worth 3.2 $25 bonds. The $25 bond value is always rounded to the nearest penny. Thus, a $5000 bond must always have a value that is a multiple of $2.00.
Interest is computed on a $25 bond using the composite rate divided by 2 for the given six month period. For individual months within the six month period, interest is computed using pseudo-monthly compounding to produce the same result after six months. For example, if the composite rate is 2.57%, the bond value after
1 month is $25 × (1 + 0.0257/2)^(1/6) = $25.05, and after
4 months is $25 × (1 + 0.0257/2)^(4/6) = $25.21, and after
6 months is $25 × (1 + 0.0257/2)^(6/6) = $25.32.
The values of a $100 bond would be $100.20, $100.84, and $101.28 after those same time periods. Note that this ignores the 3 month penalty for redemption within the first 5 years and the restriction on redemption within the first year.
Conclusion: Nothing the U.S. Treasury touches is simple.
Jose Pablo
Apr 7 2023 at 2:51pm
This is probably why the Treasury calls it a fixed rate rather than my preferred terminology of a real rate
The proper name woudl be a “fixed real rate” wouldn’t it?