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I was talking with my parents and they told me they have been buying 30 year EE bonds at $100 every 2 months with an interest rate of 4%. Because it is an EE bond, it does not pay a monthly coupon. So if we look at a single bond they bought, they would get $4 per year. Does it pay to buy the bond if we assume inflation is 2.5%? (I have seen a lot of equations use 2% as a moderate inflation rate. I am using 2.5% because it seem more realistic/robust)

($4/year * 30years) + $100 = $220 future value

(1 - 0.025) ^ 30 = 46.78% buying power in 30 years

So taking the $220 of the future dollars and multiplying it by our inflation rate gives

$220 * 0.4678 = $102.93 which is a 2.93% return over 30 years, which in turn is a 0.096% (calculation -1 + (1 + 0.0293) ^ 1/30) annual rate of return on their investment which is worse than what some banks offer.

Is there something I'm missing, something I calculated wrong (like the bond value when it matures), or did I make a bad assumption? It looks like it isn't worth buying a bond unless the coupon/rate is close to double digits.

edit: As far as I know, my parents aren't using the money that is being paid out from the bond. It is sitting in an account and they plan on withdrawing the full amount when the bond matures. So every $4 they get they technically aren't reinvesting anywhere. They have never invested in the stock market besides their 401k contributions.

This question more pertains to pure bond overall return (after 30 years) vs savings vs inflation. No reinvestment for compounding.

Well, first of all, you're adjusting the bond for inflation, but you're not adjusting the rate that banks give for inflation.

Second, it doesn't make sense to adjust money for 30 years of inflation unless you're getting it 30 years from now.

It's a bit unclear what you mean by "return". You're likely referring to the coupon amount, which is an amount of money in periodic payments. If you're getting 4% annual coupon, then you're getting $4 each year, not $120 30 years from now. You can then use that money to buy stuff, and its purchasing power will be determined by the inflation up to that point, not the full 30 years of inflation. And if you want to, you can invest the payments in something else, even another bond, so in that sense it does compound. Suppose you buy 1000 of these bonds. At the end of the year, you can buy 40 more bonds. At the end of the next year, the original 1000 bonds will give you enough money to buy 40 more bonds, and the 40 bonds you bought at the end of the first year will give you enough to buy one more bond with $60 left over. And so on. The number of bonds you have will grow exponentially.

By "return", you might instead be referring to the bond being discounted, which means that the bond is purchased for less than the face value. Discount is always compounded. However, if we are talking about discount, then there is a further complication that return and discount are slightly different. If you buy a bond for $96.15 and a year later it's worth $100, then you got a 4% return (4% of $96.15 is $3.85). But a 4% discount would mean that it would sell for $96 (the 4% is applied to the full $100). So to get a 4% return over 30 years, you would have to buy the bond for $100/(1.04^30)=$30.83, while a 4% discount would mean that the bond would be sold for $100*(.96^30)=$29.38.

If the bond outperforms inflation then it is a good investment. And the interest received from a bond can be compounded elsewhere. For instance bank savings accounts are available, often requiring a linked checking account from another bank, that pay about the same rate as the three-month Treasury Bill.

The problem with a 30-year bond is that it is a 30-year bet on inflation staying low. However, a 30-year Treasury Bond is liquid and can be traded like a stock. So an investor could speculate on an inverting yield curve with a 30-year Treasury Bond. Or shorter term Treasury Notes are available. Treasury TIP's are available.

A-rated corporate bonds are liquid enough when in an ETF.

A corporate bond investor can hedge decline in the company with put options or with margin short positions in the company stock. Basically, watch the credit rating of the bond.

Interest rate rise can be hedged with options or futures.

Treasury Securities avoid state income tax while municipal bonds avoid federal income tax. Municipal bonds also avoid state income tax in some situations and avoid AMT tax in some situations.

Treasury TIP's guarantee that the investor is not wiped out by inflation but TIP's can be hurt by interest rate rise until the time that they are adjusted by inflation.

Your edit changes your presumption:

From TreasuryDirect:

When interest is earned and compounded:

Interest is earned monthly and compounded semiannually up to 30 years.

So these bonds (EE bonds) DO compound their interest. In 30 years a $100 bond will be worth 100 * (1.02^60) = $328.

But I'm a bit confused since you say they have been buying bonds at 4% - the current rate for EE bonds is 0.10% annually, so getting 4% fixed (essentially risk-free) over 30 years seems like a fantastic deal (relative to current rates).