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

[adamaero]

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?

 

[adamaero]

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?

 

[adamaero]

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?

 

[adamaero]

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

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

The real equation uses rounding and denominations of $25: