First Republic PLOC rate = 2.25-3.50%. I Bond return = ~8%. Arbitrage opportunity?

The $10,000ish cap on I bonds limits your upside.

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Why would I not just take a Personal Line of Credit for $40K from First Republic Bank at the lower interest rate and then invest in the I Bonds to get a higher return. Isn't this a good arbitrage opportunity?

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I mean it's probably likely to yield a net excess return, but I think there are a few things that may make it not as large as the spread would indicate.

First, unless you're planning on holding them for 5 years, there will be a 3 month interest penalty. And obviously the shorter you hold them, beyond the required 12 months, the more impactful that interest penalty will be. In addition, those bonds will be taxed, at least federally, as ordinary income. Now you might be able to deduct the interest if you itemize, although I don't know if bonds qualify or not. Regardless, I'm assuming that if you can qualify for a $40,000 PLOC with those rates, you probably have a pretty decent income, so let's just assume you're in the 24% marginal bracket.

Anyways, my by calculations, and since the I-Bonds compound semi-annually, if you invested $40,000 at an 8% interest rate, that would earn $3,264 after one year. But with a 3 month interest penalty, depending on how that is calculated, that would decrease the values by about 25% (let's just say it's exactly 25%), which brings that down to $2,448 if you withdraw it after 12 months.

Now if you borrow $40,000 at a 3% interest rate (usually compounding daily), and just pay off the interest every month, that would be about a little over $1,200 in interest payments over a year (we'll just use $1,200).

Now again, income brackets can make a difference, but let's just assume it's 24%. If you can deduct the interest, then you would owe about $300 in taxes (2448-1200=1248; 1248*.24=299.52). If you can't deduct the intetrest, then you would owe about $588 in taxes (2448*0.24=587.52).

So between the borrowing costs (3% interest) and taxes, you're looking at a reduction in value of between $1500 and $1788, which deducted from the $2,448 in earnings, is a net of between $660 and $948. That leaves the excess return of 1.65% and 2.37%. Of course, that's basically a guaranteed rate of return, but that also assumes that the interest on the credit is fixed at 3%. If those are adjustable, then they will likely rise since interest rates are expected to rise, which will lower than excess return.

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Not to mention it’s a loan, so he still has to find ~3k/Mo from somewhere else to pay the note.

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Not necessarily, unless he wants to pay it off in full in a year, but I suspect he would either make the minimum payment, just pay off the interest every month, or something along those lines depending on the terms. Since it’s a line of credit, I suspect he does not have to pay it off on a fixed amortized schedule like a loan.