Let’s ‘try’ to clarify how an I Bond’s interest is calculated

Posted on September 6, 2022 by Tipswatch

You didn’t expect this to be simple, did you?

Author’s note: This article ended up being “crowdsourced” through helpful (and accurate) criticism in the comments section. The Excel formulae have been edited to reflect these better techniques. Read the comments section for more great ideas.

By David Enna, Tipswatch.com

Although I have been investing in I Bonds for more than 20 years and have been writing about them for 11 years, I never paid much attention to the “exact” way interest is calculated. I figured, I’ve got a $10,000 I Bond earning 9.62%, so in six months I’d earn $481. Close enough, right?

But if you use TreasuryDirect’s Savings Bond Calculator you may notice very slight discrepancies, even after accounting for the three-month early withdrawal penalty. The Treasury’s interest calculation is ridiculously complex and possibly a relic of ancient times when $25 savings bonds were a thing.

I don’t think TreasuryDirect ever explicitly explains the complex process, but here is a good explanation of the I Bond interest calculation from the Bogleheads Wiki:

How interest is calculated

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.

You have to love the term “pseudo-monthly compounding” and you’d have to be a genius to apply these formulae to your holdings. I mean, what the heck is a ^? But the key factor is that the interest is applied to $25, rounded to the nearest penny, then scaled up to match your current I Bond holding.

If you bought $10,000 in an I Bond dated May 2022, this would be the formula you’d use in Excel to determine the value for the first month, effective on the first day of the month after your purchase: =ROUND(25*(1+0.0962/2)^(1/6),2) . The second month would be =ROUND(25*(1+0.0962/2)^(2/6),2) . The result for month one is $25.20 and multiply that by 400 to get the investment value of $10,080. For month two it is $25.39 for a value of $10,156. I worked my way through Excel to produce this for an I Bond purchased in May 2022:

Note: What is the ROUND factor? This came from feedback from readers. If you want to incorporate rounding to the penny into the “Cumulative $25 bond value” column, you need to add ROUND to the formula, as shown in the above examples. It is important to do this if you plan on incorporating that column’s calculation into an additional formula, because this is how the Treasury does its calculations.

Read the comments section for other helpful suggestions from Excel nerds.

I used TreasuryDirect’s Savings Bond Calculator to double-check these value amounts and the October amount (actually the value on November 1) did match the total of $10,236, which is the way TreasuryDirect reports values, minus the three-month interest penalty for early redemptions. Here it is, with a $1,000 investment shown because TreasuryDirect’s calculator is for “paper I Bonds only” and won’t allow an investment input of more than $5,000.

$1,023.60 x 10 = $10,236, which matches my calculation.

But the tougher question and still a “great unknown” is what happens after six months, when the I Bond’s balance compounds? I couldn’t find a single source that could explain the exact formula. So I devised on of my own. It works, but it could be wrong. Ponder that, math teachers.

Here is the calculation for an I Bond purchased in November 2021, earning 7.12% for six months and then 9.62% for six months.

In this calculation, I updated the baseline $25 to a value of $25.89 and the new formula for May became =ROUND(25.89*(1+0.0962/2)^(1/6),2) . The formula for June is =ROUND(25.89*(1+0.0962/2)^(2/6),2) . And so on. Using this formula, I was able to match TreasuryDirect’s last estimate of value, which is for October on my chart but actually for November 1. (I Bond interest is earned on the first day of the month for the previous month.)

$10,60.40 x 10 = $10,604, which matches my calculation.

As a triple-check, I confirmed my calculations for the May 2022 I Bond values and November 2021 I Bond values on the EyeBonds.info site, which is as rock solid as any information you will find. My numbers matched up with that site’s findings.

Don’t forget …

Until your I Bond investment reaches 5 years, TreasuryDirect will always show the current value minus the latest three months of interest. You have earned that interest, but TD won’t show it to you, because if you sold out today, you’d get the amount they indicate.

In the case of the November 2021 purchase, that $10,000 I Bond is actually worth $10,856, even if TD shows you $10,604.

A Tip of the Hat to Jennifer Lammer

Lammer, CEO of Diamond NestEgg, is a YouTube video star who offers some well-explained, well-documented advice on I Bonds and other investments. She created this video to explain the complexities of I Bond interest payments and the very strange $25 baseline for all investments.

Her worksheet calculations don’t match mine — we used different starting months — but we come up with similar results, which as I love to note, would drive math teachers crazy. There is a lot of good information in this video, and Lammer makes a valiant effort to make something very complex sound simple. If anyone has further advice on this I Bond calculation, send it my way in the comments section below.

• Confused by I Bonds? Read my Q&A on I Bonds

• Inflation and I Bonds: Track the variable rate changes

• I Bond Manifesto: How this investment can work as an emergency fund

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Feel free to post comments or questions below. If it is your first-ever comment, it will have to wait for moderation. After that, your comments will automatically appear.

David Enna is a financial journalist, not a financial adviser. He is not selling or profiting from any investment discussed. The investments he discusses can be purchased through the Treasury or other providers without fees, commissions or carrying charges. Please do your own research before investing.

Posted in I Bond, Savings Bond, TreasuryDirect | 163 Comments

Video: An economist offers a common-sense look at U.S. inflation

Posted on September 4, 2022 by Tipswatch

‘We are, unfortunately, about to go through a period of prolonged, persistent high inflation.’

By David Enna, Tipswatch.com

There’s a lot of speculation in financial markets right now about an upcoming dip in U.S. inflation, triggered by a strong decline in gasoline prices. We saw some of that effect in July with all-items inflation flat for the month, even though core inflation rose 0.3%. We could see a similar result in August inflation, to be released Sept. 13.

So yes, U.S. inflation is falling from its 9.1% annual peak in July, and will probably continue to gradually decline. But by how much, and how fast? How long will it take to get to the Federal Reserve’s target of 2% annual inflation?

Here’s a clearly explained outlook from Campbell Harvey, a Canadian economist who is professor of finance at Duke University and a Research Associate of the National Bureau of Economic Research in Cambridge, Massachusetts. In the video, Harvey explains why statistical and structural evidence points to U.S. inflation remaining at an annual rate of of at least 6.2% by the end of the year, even if deflationary pressures continue for several months. A more realistic number might be above 7.0%, he suggests.

“It’s kind of obvious looking at the data, but a lot of people don’t pick it up, is that we’ve already had year to date … 6.3% inflation. So if you think that inflation is going to end the year at 2 or 3 percent, it means that we are going to have strong negative inflation. … And I think that is very unlikely.”

Harvey also points out important changes in the way inflation was calculated 40 years ago versus today. The key point is that changes in the shelter index (which is weighted to be about 32% of all-items inflation) were designed to smooth out volatility, and that means inflation is printing lower than reality. The result: “There is more to come. And it is because of this smoothing.”

“The point is, this inflation has already happened, but it is not reflected in the CPI. And it will be reflected in the next year, or maybe longer. So anybody who is telling the story ‘oh well, this is just supply chain or geopolitical risk and we’ll quickly be back down to 2, 3 percent’ … No. You have to look at the actual structure of how inflation is calculated.”

It’s an excellent video. Give it a watch.

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Feel free to post comments or questions below. If it is your first-ever comment, it will have to wait for moderation. After that, your comments will automatically appear.

David Enna is a financial journalist, not a financial adviser. He is not selling or profiting from any investment discussed. The investments he discusses can be purchased through the Treasury or other providers without fees, commissions or carrying charges. Please do your own research before investing.

Posted in Federal Reserve, Inflation | 10 Comments

What’s up with those crazy real yields on ultra-short-term TIPS?

Posted on September 2, 2022 by Tipswatch

By David Enna, Tipswatch.com

Update: This TIPS matured Jan. 15, 2023. How did it work as an investment?

Just about every month, I get emails or comments from readers pointing out what appears to be extremely attractive real yields on very short-term TIPS — especially those maturing in less than a year. My usual response is that these real yields get highly exaggerated as maturity nears and only one coupon payment remains.

I’ll admit I don’t fully understand the mechanics of the quoted real yields when TIPS are down to the final months. But I assume — and I am pretty sure I am right — that the market is pricing these TIPS correctly. This month, we have another example, and I decided to take a walk-through look at this possible investment, CUSIP 912828UH1:

CUSIP 912828UH1 was originally issued as a 10-year TIPS on January 15, 2013. I wrote about this TIPS back then, believe it or not. It was in the early years of misery for TIPS investors, with this TIPS getting a real yield of -0.630% and a coupon rate of 0.125%. Now, as it is approaching maturity, it has built up an inflation accrual index of 1.28372 as of September 1. And on Thursday it was trading with an “apparent” real yield of 4.047%, according to the Wall Street Journal’s closing statistics.

So, an investor in this TIPS will be purchasing 28.3% of additional principal above par, and that principal is not protected against deflation in future months. In fact, the principal balance of this TIPS will decline 0.01% in September, based on non-seasonally adjusted inflation in July. We could see more declines in October and November, if falling gas prices create deflationary numbers for August and September, which seems possible.

I went onto Vanguard’s trading platform and entered a $10,000 purchase of this TIPS (for example purposes only — I didn’t complete the purchase). Here is what the order sheet showed Thursday afternoon:

Note that a purchase of $10,000 of par value will cost an investor $12,660.82. Here’s a rundown on the basics of that investment, and note that my total cost is off from Vanguard’s by 5 cents, and I have no idea why:

Because of the discounted price, an investor is getting $12,837 of principal from a $12,661 investment, which is attractive. But just how attractive? It’s hard to say, because the final payment at maturity on January 15, 2023, is going to depend on how hot or cold inflation runs through November. The Treasury market is speculating that inflation will decline or at least remain muted through the end of the year, which could be accurate. Or could this be recency bias based on the recent collapse in oil prices?

Here is my speculation on a “muted inflation” scenario for this TIPS, with inflation falling -0.05% in August, then remaining flat in September, rising 0.1% in October and then 0.2% November. (This TIPS will get an inflation adjustment of 15 days from November inflation in its final month.)

If things work out this way — pure speculation — the investor on September 1 will have invested $12,660 and will get a return of about $12,863 on January 15.That’s a gain of $203, which isn’t shabby for a 4 1/2 month investment. It’s an annualized return of about 4.38%. Not quite up to I Bond standards, but better than similar nominal Treasury yields, which are hanging just above 3%.

Based on this rough look at CUSIP 912828UH1, it seems like a reasonable investment, given the discounted price. The investor picks up the risk of the 28% inflation accrual, which could get depleted if deflation becomes a “thing” in the next several months. My example may be too optimistic. Who knows? The market is clearly signaling a belief that inflation will be very low, or negative, through November.

Would I buy it? No, I am not interested. It’s just too complex to be worth the trouble. This example was simply meant to demonstrate the “logic” of today’s market, which might be logical, or possibly crazed.

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Feel free to post comments or questions below. If it is your first-ever comment, it will have to wait for moderation. After that, your comments will automatically appear.

David Enna is a financial journalist, not a financial adviser. He is not selling or profiting from any investment discussed. The investments he discusses can be purchased through the Treasury or other providers without fees, commissions or carrying charges. Please do your own research before investing.

Posted in Inflation, Investing in TIPS | 17 Comments

Yes, I am still traveling (and news is breaking out all over the place)

Posted on August 28, 2022 by Tipswatch

By David Enna, Tipswatch.com

I woke up today in rainy Sitka, Alaska. Rain is not an an unusual thing in Alaska in August, I have learned. It has rained every single day on this trip, which started August 14. Rain is in the forecast for the rest of the trip.

But hey, we’ve seen some rainbows … and bears, moose, eagles, ravens, caribou, reindeer … along the way. No otters yet, I want to see an otter.

I know a lot of news has been breaking out in the last two weeks, which always seems to happen when I am traveling, especially in places with little or no internet. From the little I can grasp, it appears that Fed Chairman Jerome Powell finally set the markets straight on his intentions: To fight inflation until inflation is defeated. That was what Powell should have said, and the markets should have expected it.

But, no, the markets still had a lingering belief that the Fed would step in to save the stock market. But that can’t happen while U.S. inflation is continuing at an annual rate of 8.5% and raging even higher across the globe.

So for inflation-protected investments, what has happened in the last two weeks?

  • The 5-year real yield started at 0.29% on Aug. 15 and closed Friday at 0.47%.
  • The 10-year real yield started at 0.35% and ended at 0.47%.
  • The 30-year real yield started at 0.89% and ended at 0.85%.

These aren’t dramatic moves, but the current yields keep the 5- and 10-year TIPS as attractive investment possibilities. There’s a 10-year TIPS reopening auction coming up on Sept. 22, followed by a new 5-year auction on Oct. 20. Both of these could be attractive, especially since the 5-year real yield should track higher with any upcoming Fed moves in September.

I’m not connected enough right now to give an opinion on anything else going on. If you you have ideas, comments or theories, post them in the comments section below.

I will be back home in North Carolina mid-week, as long as I survive whatever Covid protocols are thrown at me in the last days of the trip. In closing, here’s a view of Denali National Park:

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Feel free to post comments or questions below. If it is your first-ever comment, it will have to wait for moderation. After that, your comments will automatically appear.

David Enna is a financial journalist, not a financial adviser. He is not selling or profiting from any investment discussed. The investments he discusses can be purchased through the Treasury or other providers without fees, commissions or carrying charges. Please do your own research before investing.

Posted in Investing in TIPS | 27 Comments

30-year TIPS reopening gets a real yield of 0.92%

Posted on August 18, 2022 by Tipswatch

By David Enna, Tipswatch.com

The U.S. Treasury’s reopening auction today of CUSIP 912810TE8 — creating a 29-year, 6-month Treasury Inflation-Protected Security — got a real yield to maturity of 0.92%. This was the highest yield for any auction of this term in more than 2 years.

It looks like the auction was met with strong demand, with the real yield coming in a few basis points lower than where this TIPS was trading right before the auction’s close. The bid-to-cover ratio was 2.69, also an indication of good demand.

This TIPS had an originating auction in February, where it got a real yield of 0.195% and a coupon rate of 0.125%. Thursday’s auction demonstrates how much real yields have surged higher in 2022. Investors paid an adjusted price of about $84.61 for about $106.40 of principal, after accrued inflation is added in. This TIPS will have an inflation ratio of 1.06397 on the settlement date of Aug. 31.

The inflation breakeven rate, by my estimate, was 2.21%.

I am traveling this week and I am about to go on a trek into Alaska’s Denali National Park, so I will just close with the usual graphs … Real yields, inflation breakeven rate, and auction history.

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Feel free to post comments or questions below. If it is your first-ever comment, it will have to wait for moderation. After that, your comments will automatically appear.

David Enna is a financial journalist, not a financial adviser. He is not selling or profiting from any investment discussed. The investments he discusses can be purchased through the Treasury or other providers without fees, commissions or carrying charges. Please do your own research before investing.

Posted in Investing in TIPS | 5 Comments