# Rate of return on an Life Insurance Annuity

So as I approach retirement age, many people are out there suggesting annuities as a way to fund retirement. It's seductive, as they typically have around a 6% payout, that is 100K buys you 6k worth of income for the rest of your life.

However, what they fail to mention is that when you die they keep the principal paid in. So on the surface it looks like you are getting a 6% return on your investment, but for your heirs/estate that is not the case.

So assuming you pay in 100K, and live for 25 years, you would get a total of 150K for your 100K. But since they keep that initial 100K, your real gain is only 50K. This comes out to a 2% rate of return. But that is not totally correct: it is less than that as the 6K in year 25 is worth much less than the 6k in year one.

I feel like the real rate of return is around 1.75% given the above stats, but I am not good enough to do the math. I have not found a formula which accounts for the life insurance company keeping the money after you die.

Anyone have such a formula?

• A word of warning. The people suggesting annuities are likely the people SELLING annuities with a huge commission. They don't make sense for many people.
– JohnFx
Feb 26 at 14:40
• Annuities provide you a guarantee of income. They are not an investment product, as such a rate of return doesn't really make sense, as they eliminate the risk that a typical rate of return would need to compensate you for (ie the risk of going to zero), they also eliminate all of the administration burden of investing (and ensuring your estate knows where all your investments actually are). Feb 27 at 10:52
• You mention "Life Insurance Annuity" in the title -- note that there's a bit of ambiguity there, as some life insurance policies can apparently pay out an annuity as a death benefit. The body of the question appears to be asking about regular annuities. Feb 27 at 22:38
• "I cannot imagine a good scenario for one" -- I'm not a financial planner and not yet near retirement age. However, I can imagine that some folks have long-term, relatively stable recurring debts (mortgages, assisted living/nursing home expenses, etc.) and just want peace of mind that they never have to worry about coming up with it. It might also be appealing for forcing your own hand in legacy planning: "I want to leave 50% of my wealth behind" --> buy an annuity with 50%, give the rest away as you please, and you don't have to worry about rates of return or lost income Feb 27 at 22:48
• @thehole: Possibly even better, see if your favorite organizations offer Charitable Remainder Funds, which is basically a mix of annuity and donation. I've seen these offer to pay back 5% of the principal per year, with a large tax deduction when you first give them the money and some tax advantages for the first 10 years of money coming back. You can get better payments from a pure annuity, but depending on you tax situation this may be a decent deal. And it's better for the charity than waiting to be given that money in your will. Feb 28 at 5:43

your real gain is only 50K.

You are correct about the nominal gain in dollars (ignoring inflation). It is \$50,000.

This comes out to a 2% rate of return. But that is not totally correct

This is incorrect in every way. The nominal gain is \$50,000 but you can't just say that the "average interest" is \$50,000 / 25 / \$100,000, because you limited yourself to 25 years only. It became an Annuity, not a Perpetuity.

The actual nominal interest rate is 3.397% (ignoring inflation). In this calculator, you paid \$100,000 at the beginning, got \$6,000 each year for 25 years, and is left with \$0 at the end of 25 years, and made a nominal gain of \$50,000.

You can imagine that you are a bank lending \$100,000 to the insurance company, and the insurance company is paying you back \$6,000 for each of 25 years (last year is still \$6000 payment, not \$100,000). The \$6,000 each year includes both principal component and interest component. It is literally a loan that needs to use Amortization Table.

In fact, if you live long enough (e.g. 100 years since buying), the annuity becomes a perpetuity, where the actual nominal interest rate is very close to 6.000% (ignoring inflation).

So how do you account for inflation? There are 2 ways:

1. You don't. You simply compare the expected nominal interest rate of 2 products, i.e. 6% annuity of 25 years vs 25 years United States Treasury Fixed Interest.

2. You compare the expected nominal interest rate of 2 products above and deduct the Federal Reserve target inflation of 2% from both products. This is meaningless in making decisions. One product's inflation won't be magically different from another product's inflation.

For reference this is the 6% annuity product:

Years Alive Nominal Interest Rate
5 -30.191%
10 -8.351%
15 -1.289%
20 1.803%
25 3.397%
30 4.306%
35 4.860%
40 5.215%
45 5.449%
50 5.608%

Given that long term United States Treasury Fixed Interest rate is around 4.5%, I would say that you need to be alive for around 33 years to break even.

*I forgot to say that there is no "formula" for interest rate per year. You need to rely on the algorithm of the Financial Calculator or Excel. Alternatively, binary search to solve an equation. In Excel it is:

``````=RATE(25,6000,-100000,0,0)
``````
• I don't feel like this math is right, Lets assume I can get a 25 year bond at 3%. If I buy 100K of bonds, after 25 years I will have 175K. I am far better off doing that! So 3.4% seems wrong. Feb 27 at 14:23
• @PeteB. You comment is partially correct. If you buy an actual bond that pays 3%, the nominal interest amount and final amount in total seems to be a lot more than a 3.4% equivalent annuity. However, in order to compare apples to apples, you must perform bond trading actions to mimic the payment schedule of the 6% annuity. That means, after getting 3K from the bond each year, you also SELL about 3K worth of bond each year, this would give you 6K cash flow. As you sell this additional 3K worth of bond, your "compounding effect" of the 3% is lessened. After all, you NEED 6K to survive. Feb 27 at 14:57
• @PeteB. This way, the ending value of the bond would also be ZERO. See this Excel screenshot for 3% bond. It can't even sustain 25 years; At 23.5 years it's out of money. Whereas if you use a 3.397% bond, it can sustain 25 years. i.stack.imgur.com/1bEvL.png The amount of "selling" increases gradually. Feb 27 at 15:08

See other answers about annuities They are very much an insurance product; you are paying someone to guarantee you an ongoing income no matter what investments are doing, for your entire life and/or the lives of everyone on the policy if you have written it to cover survivor(s?). They have run the numbers and are willing to bet that the market does well enough and/or you (and survivors) will die early enough that they can not only afford this specific payment but will probably make a significant profit. You are taking the opposite side of that bet, which their statistics say is probably the losing side.

You are also betting that the contract survives; if the insurer goes bankrupt their insurance may not be good enough to fully meet their commitments. (Then again, that's not too much more risk than of a bank failing and having to rely on the FDIC. Large insurers are the size of, and sometimes are, large banks.)

As always, the alternative is to self-insure. Just set up an investment strategy that you have sufficient confidence in that you like the odds better. Long-term "market rate of return" has been around 8%, and it isn't hard or especially risky to get about that return, if you have the patience and reserves to wait out bad years. There certainly is risk, but as always you need to balance that against reward.

Run your own numbers for both options, and consider whether the security is worth the cost. And shop around; each insurance company runs its own numbers and may make substantially different offers. If are considered a preferred risk, some companies may offer more. I got a better than average offer through my employer's retirement plan, for example, apparently because technogeeks who make it to retirement are apparently considered slightly lower risk than the general population.

In my case, I have purchased a smallish annuity (costing me around US\$100k) to supplement the social security safety net (when I start taking that), but am really planning on self-insuring and living on my investments. Your balance points may be completely different. Remember to consider legacy if any when deciding how much to buy.

"Live long and prosper!"

• -1: It's an insurance product, correct. You incorrectly characterise what the insurance company is doing ("probably make a significant profit"). They are spreading the risk across many people, some people will die early, some will die late. The insurance company is also spreading the risk over time and are exposed to advances in medicine allowing people to live longer (ie making their assumptions on sale incorrect). They are also paying for all of the administration of the payments and tracking. The profit margins in (life) insurance are typically 2% - 8%. Feb 27 at 10:42
• @illustro What exactly is "incorrect" about that characterisation? Nobody is doubting what an insurance does, and you also don't contest that they do it for profit. The only point of contention seems to be whether you consider 2% - 8% "significant" ... Feb 27 at 13:02
• If you think the surcharge is too high, you don't buy it. Sufficient numbers of people find it a useful product worth it's cost that the companies stay profitable, and most of the buyers aren't idiots. Like any insurance product shop around for the best deal, compare it to self-insuring, and decide how that balances out for you. Feb 27 at 15:16
• And, yes, all of that plays into their decision of what to offer you, just as it does for life insurance, auto insurance, flood insurance. So what? It still comes down to your choice of whether it it is worth the price FOR YOU or not. Feb 27 at 15:19
• @xLeitix I detailed exactly what I described as incorrect. "probably making significant profit". Apple makes a significant profit (Net income before taxes/Net income = 26.9bn/96.9bn = 27.7% in September 2023). Walmart, globally, had a gross profit rate of 24+% in 2020, 2021 & 2022 & 23.5% in 2023. Calling a 2-8% profit margin significant in this context mischaracterises what is actually going on. Feb 28 at 13:29

Other than the math error as base64 illustrated, your intuition is correct. Your actual return starts negative and climbs to 6% the longer you live.

It's important to remember that annuities are not investments, they are insurance. Just like life insurance protects you from dying too early (leaving your heirs with debts or losing a source of income), annuities are insurance against dying too late, meaning you outlive your retirement savings.

Also like any insurance, you should not expect to make money off of them; they are priced such that the insurance company, when issuing thousands of annuities, makes a profit on average. Some people will make a higher return by living a long time, some will be unlucky (in 2 ways) by dying early.

what they fail to mention, is that when you die they keep the principle paid in

If your planner "fails to mention this" then you need to find a new planner. They are probably only interested in selling you products rather than helping you plan for your future and protect from unplanned events. A good planner should explain all of the details of what you are buying, why you are buying them, and what the risks are.

If it's just friends or acquaintances suggesting this, then that are just uninformed. Which is fine, I am uninformed on plenty of things; I just try (sometimes unsuccessfully) to inform myself before making decisions that affect me or my family's future significantly.

There are other actual investments that can give you close to 6% return on average and preserve at least part of the capital invested. They may go down in value over time but you will not lose everything at death. Ask your advisor about fixed-income mutual funds (which invest in bonds, they do not guarantee a specific rate of return themselves) that are relatively safe (or at least safer than something like the S&P 500) and provide periodic income. If you don't need the income until you die, you can reinvest it and keep the the principal up until you do need the income.

• two comments re this: "You will not lose everything on death.": 1. instead you may lose everything when the market goes down and you are still alive. 2. by definition, when you die, you can no longer "lose" anything. Your estate loses some value (maybe), but you as the annuitant don't actually lose anything. Feb 27 at 10:46
• "1. instead you may lose everything when the market goes down and you are still alive." - well, having actually accomplished something close to this during the dot-com bust, I can say it does not happen by accident - it takes hard work and determination to lose everything in the market. You're contrasting that to a 'loss' that is inherent in an annuity contract. Feb 27 at 17:07
• It would be great if life insurance actually protected you from dying too early ;) Feb 29 at 11:23

I’m in the situation and looking myself. Annuity has the benefit that the money is guaranteed to never run out until the moment you die. In a savings account and drawing out money, you may still have \$100,000 in the bank the moment you die, which is useless to you. Or you run out of money 10 years before you die, which is worse than useless.

The insurance company will make profit from you individually if you die early and lose money on you individually if you live for long. Since they have 10,000 customers they pay out to make some profit on average. For you as an individual, “some profit on average” is no good.

The only thing you can do is comparing offers from different companies and with different terms. The simplest terms would be “pays until you die”. I could chose “continues paying my wife until she dies, at 100%, 66% or 50% of my rate”. I could chose “pays X to my heirs if I die within ten years” to avoid the annoyance of signing the deal and being run over by a car the next day. You can have an automatical annual increase.

Each set of terms changes the payout. Your only choice is comparing different payouts, different insurance companies, and accept the best offer that you find acceptable.

The biggest variable is how long you live, and you cannot change that.

• For me, I'd rather use 200K to by dividend paying stocks that pay out 3% and live off of that. Leaving money to my heirs is important to me and I would rather work longer to do it. I have no desire to write the insurance company into my will. Feb 27 at 14:25
• Well, that’s entirely up to you. My priorities are my wife and myself. And I very much hope that my heirs would be in their sixties and have planned their own retirement. Feb 28 at 2:03
• And as I mentioned, you can have all kinds of different contracts, at least in the UK. The big choices are whether and how much they continue paying to my wife if I die, and whether and how much they will pay to my heirs. If course the more the pay out, the less you get every month and vice versa. Feb 29 at 15:37

If we say that the "fair" discount rate is d, then after n years, your principal will be worth Pd^n.

For instance, suppose we use a discount rate of 96%, and you die after 25 years. Then that means that there's \$100*0.96^25 = \$36k of present value that's going away. If we subtract that from the original amount, we find that we have \$64k of present value left. That is, you're only getting 64% of that 6%, so your effective interest rate is 3.84%.

Now, a discount rate of 96% corresponds to an interest rate of 4.17%, which is more than the effective interest rate. A "fair" discount rate would get you an effective interest rate that matches the discount rate. So my initial guess of 96% being a fair discount rate wasn't quite right. If you want to get the exact value, you can put the math into Excel and do goal seek, and you'll find that the proper effective interest rate is 3.3976%.

There's no closed form formula for this; any calculator is going to use numerical methods.