Savings Bond interest rate calculations

Wednesday, August 31st, 2011
Categorized as: Savings Bond interest ratesCurrent value of a US Savings Bond

If you want to check the Treasury’s Savings Bond interest rate calculations, start by reading my post on the three reasons it’s hard to match the Treasury’s calculations.

If you’re still interested in the math after reading that, here’s how to get the Treasury’s exact numbers.

The Treasury bases all of its calculations on hypothetical $25 bonds. The investment for a $25 EE bond would be $12.50 and for an I bond would be $25. This is the initial value for the following calculations.

For the first rate period, the actual value at the beginning of the month after issue is:

Initial Value * (1 + (rate/2) )^(1/6)

For the rest of the months in the rate period, change the final exponent to 2/6, 3/6, and so on up to 6/6. Round these values to two decimal points. This gives you the actual value of a hypothetical $25 bond of either series for each month of the first rate period.

For the second and later rate periods, the calculations are exactly the same, but now the initial value is what the bond was worth (rounded to two decimals) at the end of the prior rate period.

Next you have to blow these numbers up to the denomination of your bond. A $100 bond, for example, is the equivalent of four hypothetical $25 bonds, so you’d have to multiply the value the calculation gives you for a $25 bond by four.

Finally, you have to allow for the three-month interest penalty. Until a bond is five years old, its redemption value is what its actual value was three months earlier. Our Savings Bond Calculator, like all other Savings Bond Calculators, shows redemption values, not actual values.

Month-to-month interest can seem to jump around much more than it should, but it’s all just magnified rounding errors. The Treasury’s goal is to make sure that someone who has invested $10,000 in 200 $50 bonds earns exactly as much as someone who owns a single $10,000 bond. The month-to-month interest jumps are a result of this denomination exactitude.

Update 8/31/2011: In a discussion on the Bogleheads forum, sscritic points out that the above formula is incorrect (because it compounds the monthly interest). The correct formula would be:

Initial Value * (1 + (rate/(m/12))), where m is the number of the month (1 to 6)

Typically, after rounding, both formulas give the same result, but if the results are different, sscritic’s method gives the accurate result.

Update 9/5/2011: Whoops. As the conversation continued, #Cruncher demonstrates that the Treasury really does use the original formula I presented above, although all agree the second formula better describes what the Treasury says it does.

sscritic says:

Compounding monthly means that you get less interest in the early months and more later (that’s what compounding does). With straight line interest, the graph is a straight line; with compound interest, the graph is a exponential curve (base > 1 and positive exponent, so convex). If the end points match, the compound interest curve will always be below the straight line interest line.

What this means is that calculating the monthly redemption value using compounding rather than straight-line interest works to the Treasury’s advantage.

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9 Comments

On November 12th, 2008 Davin said:

When you buy a savings bond, are the rate fix or variable? If you buy a bond today with the rate at 5%, will it change next year? or it’ll stay 5% until customer redeem the bonds?

On November 13th, 2008 Tom Adams said:

Davin - it depends on whether you’re talking about Series EE Savings Bonds or Series I Savings Bonds and whether you’re talking about a new bond issued today or one issued in the past.

With today’s Series EE, the rate is fixed, although it’s currently 1.3%, not 5%. However, for Series EE Savings Bonds issued before May 2005, rates are variable.

With Series I, there is a fixed rate component, currently 0.7%. The rate of inflation is added to that. Currently that rate is 4.92%, for a total rate of 5.64% the first six months you own the bond. Every six months after that the rate is adjusted to match the inflation rate.

Tom Adams

On November 14th, 2008 Dan said:

Also EE Bonds, if held for a full 20 years, will get a one-time bump in value to double the purchase price. This implies a 3.5% annual rate over the full 20 years, if held that long.

(Not saying that EE bonds are a good deal, just pointing out the effect on the otherwise fixed rate.)

On January 13th, 2009 Gail said:

I have 4 mature Series E Savings Bonds that I would like to redeem. They are qty 3 for $25 and qty 1 for $50. What is my interest/tax on these?

On January 14th, 2009 Tom Adams said:

Gail - use the Savings Bond Calculator at the top-right of this page to determine how much of each bond is interest.

The amount of tax you’ll have to pay on that interest depends on your other income - you add the interest to your tax return for the year you cashed the bond - and can vary from 0% to 35%.

Tom Adams

On January 17th, 2009 Donnie Adams said:

Do Series I bonds have anything like the one time 20 year bump-up in value like the Series E bond?

On January 19th, 2009 Tom Adams said:

Donnie - No, that feature applies only to EE bonds.

Tom Adams

On March 4th, 2010 ann said:

Hi Tom,
I now realize after reading more on your website that we did not inherit a stepped-up basis on the EE bonds inherited from my mother-in-law. However, we could have included the interest earned on my MIL’s tax return in earlier years.

My mother-in-law passed away in 2008 and had taxable income in 2008 and 2007. In 2006, my mother-in-law had -$17,000 of income. Would it be possible to amend her 2006 return to include the interest earned on the bonds through 2006, and then include that previously taxed interest on Schedule B of our 2009 return?

How do I calculate the interest income on the bonds through 2006 if we can amend her 2006 return to include this interest income? She had four $1,000 EE bonds and one $10,000 EE bond that were purchased on Jan 8, 1992.

On March 5th, 2010 Tom Adams said:

Ann - You can use the Treasury’s Savings Bond Calculator to determine the value of the bonds as of any date since Jan 1996.

However, I don’t know if you can amend the return of someone who has passed away just to change the Savings Bond accounting method. But if you can, you’d have to amend the 2007 and 2008 returns too, to add the Savings Bond interest earned in those years. This is a pretty technical question, I suspect most tax advisors won’t know the answer either, but I don’t know who else you could ask.

Tom Adams

Comments Closed

June 1, 2010

After six years, over 400 posts, 3,680 real comments, and over 90,000 spam comments (thank you, Akismet, for making managing a blog with comments possible), I am closing public comments on Savings-Bond-Advisor.com. I will contine to update the main articles on this site, but not the comments.

Virtually every question about Savings Bonds has been asked and answered on this site multiple times. Use the search feature (see the box in the gray area near the top of this page) or the detailed menu on the lower part of the home page to find the information you're looking for. If you have a copy of Savings Bond Advisor, you can ask me a question here.

Tom Adams

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