# Are bonds worth the investment since they don't compound?

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.

• but that bank account earning <<1% is losing money against inflation. Commented Dec 28, 2018 at 18:04
• That \$4 per \$100 bond can be invested. if they are doing this 6x per year, and they have doing this for lets say 5 years. they have 30 bonds throwing \$4 a year which allows them to buy an extra bond every year. Commented Dec 28, 2018 at 18:08
• What you're missing is that you're comparing an inflation adjusted bond return with a non inflation adjusted bank account. Currently, you can get 2.25% in a MM fund. 4% from a bond is better than 2.5% from a MM. Commented Dec 28, 2018 at 18:09
• Often you buy bonds for current income. Are your parents spending the coupon or saving it? Commented Dec 28, 2018 at 18:45
• @BobBaerker Thank you for that. I see that I was not comparing apples to apples Commented Dec 28, 2018 at 19:16

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.

• I upvoted but the last paragraph is wrong (or at least confusing). You seem to be calculating the present value of a zero-coupon bond with a 4% discount rate, which is very different than a bond with a 4% coupon. Commented Dec 28, 2018 at 19:30
• @DStanley Yeah, there's a bit of a conflict between being precise and clear. Explaining the difference between return and discount makes the answer more rigorous, but also more confusing. Commented Dec 28, 2018 at 19:44
• This does clear some stuff up. I invest in the stock market and haven't touched a bond yet so I am not knowledgeable as to how they fully work. When I say "return" I am talking about how much money I have in the end along with how much buying power I have. I updated my question to be more clear Commented Dec 28, 2018 at 19:55
• @Acccumulation Also, It might be good to mention that parents have EE bonds which I just found out don't pay a monthly coupon. Commented Dec 28, 2018 at 20:06

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).

• I guess I don't know enough about them. I found out that EE bonds existed after I asked the question thinking they were regular bonds. My parent's showed me their paper receipts and they say 4%. I think they bought them from the late 80s to '06. And the link I added said you could buy them for half price when you bought them on paper, which is what my parent's paper showed (value of 100 bought at 50) which really confused me when I first saw it. Commented Dec 28, 2018 at 21:20
• @rhavelka Ahh ok that would be a reasonable rate in the 80's. There are many variations of bonds (both government and corporate) so having some that compound interest without paying it out is not unreasonable. Commented Dec 28, 2018 at 21:21
• The subject changed to EE-bonds and became confused. However, this new subject is interesting as EE-bonds look like a bad deal while I-bonds look like a very good deal. There is a \$10,000 yearly limit on the I-bonds. Commented Dec 29, 2018 at 19:12

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.

• "If the bond outperforms inflation then it is a good investment. " That's not true when taking into consideration opportunity costs and risk. Commented Dec 28, 2018 at 18:53

Taking just your simple question and not the explanation: That surely depends on the interest rate the bond is paying relative to other potential investments. If someone offered me a 5 year investment with 1% interest with compounding, and someone else offered 20% without compounding, clearly the second is the better investment.

If you're talking specifically about government EE bonds, yes, the return is small. But the risk is also small. This is a classic investment decision: Do I want high promised return but with a high risk that the issuer will default and I'll get little or nothing, or a lower promised return but with a high probability that in fact I'll get what's promised?

The US federal government has, to the best of my knowledge, never defaulted on a debt. Government bonds are backed by the taxing power of the federal government, and for the feds to default would mean that there had been a massive depression so big that the government couldn't even collect enough to pay its debts, or that there was some huge political upheaval. In either case, you'd probably be much more worried about defending yourself from the mobs rioting in the streets than about a faulted bond.