Savings Bond interest rate calculations
Wednesday, August 31st, 2011
Categorized as: Savings Bond interest rates • Current 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.
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.