B What's the equation for an I Bond? (compounded semi-annually)

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I Bonds are compounded semi-annually, and the overall rate is calculated using the formula: Overall Rate = [Fixed interest rate + (2 x bi-annual inflation rate) + (Fixed interest rate x bi-annual inflation rate)]. For a scenario with a 9% rate for the first six months and a 6% rate for the next, the composite rate for the first period is 9%. The calculations for interest earned involve both simple interest for the first six months and compounded interest for the next six months, ultimately leading to an ending balance based on these rates. The discussion highlights the complexities of calculating I Bond returns, including considerations for rounding and specific denominations.
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I Bonds are compounded semi-annually. What's the equation for an I Bond?
https://www.wallstreetmojo.com/series-i-bond/

Overall Rate = [Fixed interest rate + (2 x bi-annual inflation rate) + (Fixed interest rate x bi-annual inflation rate)] Say the first 6 months is 9%, the next six months is 6% and the fixed interest rate is 0.1% for both. What is the final rate?

Is it the overall rate done twice, added and then divided by two?
 
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Wait, the composite rate is already 9% as said here: http://eyebonds.info/ibonds/10000/ib_2022_08.html

So what equation uses that composite rate of 9% for the first six months. So is that the simple interest rate for six months, and then it's compounded; then that gains simple interest for another six months?
 
Say I bought $1000 worth of I bonds on August 1, 2022. For months 1-6, the overall interest rate is 9.62%.
For months 7-12, say the overall interest rate is 6%.

SI = Principal_1*Rate_1*Time

1000*9.62%*6 = SI

CI = Principal_2*(1 + Rate_2)*Time − Principal_2

SI*(1+6%)*6 - SI

Like this or?
 
  1. For first 6 months: I = PRT. Interest = ($10,000) * (3.54%) * (0.5 years) = $177.
  2. For next 6 months: I = PRT. Interest = ($10,177) * (7.12%) * (0.5 years) = $362.
  3. 10000(1+[0.5*3.54%+(1+3.54%*0.5)*7.12%*0.5]) = Ending balance = $10,177 + $362 = $10,539.


  1. $1000*9%*0.5 = afterSix = 45
  2. (1000+afterSix)*6%*0.5 = 31
  3. P*(1+[r1*0.5+(1+r1*0.5)*r2*0.5])
= $1076

---

(9%+6%)/2 is close enough :)

The real equation uses rounding and denominations of $25:
 
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