Will Inflation And The Stock Market Conspire To Kill The 4% Rule?


A recent WSJ headline sent chills down the backs of every retiree—”Cut Your Retirement Spending Now, Says Creator of the 4% Rule.”

In the article, the WSJ quoted the father of the 4% rule, William Bengen, as saying that “there’s no precedent for today’s conditions.” Stock and bond prices are still at record highs. Mix in a reference to 8.5% inflation, and the WSJ starts to sound like an insurance salesperson pitching indexed annuities.

So are things really that bad? And do retirees need to rethink the 4% Rule? I don’t think so, and here’s why.

The 4% Rule is Now the 4.4% Rule

In the article, Mr. Bengen said he believes a safe initial withdrawal rate is 4.4%. Yes, that’s an increase from his initial findings in his 1994 paper.

In his 1994 paper, he assumed retirees invested in the S&P 500 and intermediate Treasury bonds. That’s it. Since then he expanded the asset classes to include mid-cap, small-cap, micro-cap and international stocks. This diversification caused him to increase the safe withdrawal rate from 4% to 4.7%. Because of the unprecedented conditions noted above, however, new retirees might want to start at 4.4%, he said.

As far as I can tell, the 4.4% rate is not based on data. Still, it represents a 10% increase, not decrease, from his initial 4% rule. That doesn’t sound so bad.

“The combination of 8.5% inflation with high stock and bond market valuations make it difficult to forecast whether the standard playbook will work for recent retirees,” said Bengen. He’s even gone so far as put 70% of his personal portfolio in cash. When the father of the 4% rule cashes out, shouldn’t we?

I don’t think so. For starters, it’s important to understand how Bengen developed the 4% Rule. He examined 50-year retirement periods dating back to 1926. For each, he identified the highest withdrawal rate one could take in the first year of retirement, adjusted for inflation in subsequent years, without running out of money for at least 30 years.

As you might imagine, every year had a different initial withdrawal rate. Some years the starting rate was twice what it was in others. Here’s the key point. He didn’t average all of these initial withdrawal rates to come up with the 4% rule. He took the absolute worst year—1968.

Here’s more on how the 4% Rule works.

What does this mean? It means the 4% Rule has survived the stock market crash of 1929, the Great Depression, WWII, the Korean War, the Vietnam War, the inflation of the 1970s and early 1908s, the 1987 market crash, 9/11, the Great Recession and Covid-19.

Stock Prices

No matter how difficult past times have been, current conditions feel awful in ways that history never can. One need look no further than Robert Shiller’s CAPE (cyclically adjusted price-to-earnings ratio) of the S&P 500 to raise concerns. It stands at roughly twice its average and at historic highs. It’s only been higher once, and that was during the tech bubble.

Yet as “unprecedented” as this may seem, it’s not for two reasons. First, most portfolios don’t have the same PE as the S&P 500, even if measured using CAPE. Add in mid-cap, small-cap and international stocks, and the PE comes down significantly.

Second, and more important, the CAPE of the S&P 500 would fall to average with a 50% decline in the S&P 500. This wouldn’t be fun, but it wouldn’t be unprecedented, either.

As noted above, the market lost 90% to kick off the Great Depression. And going back to the tech bubble, the market lost 9%, 12% and 22% from 2000 to 2002. That’s not quite a 50% total loss, but close. And from peak to trough during the Great Recession (2007-2009), the market lost more than 50%. The 4% Rule survived like a cockroach.

Bond Prices and Inflation

Bond yields were at historic lows. I say “were” because that’s no longer the case. The roughly 3% yield on the 10-year Treasury is still below average, but there are plenty of years dating back to the 1800s when they were lower. And when Bengen published his 1994 paper, TIPS were three years away and the first I bond was still four years away. So at least now we can keep up with inflation.

Here’s the key. The 4% Rule has survived Treasury yields as low as 1 to 2%. It also survived inflation of more than 13% and a decade of inflation at 6% or higher. And like the Energizer Bunny, it keeps going and going (or ticking for you Timex fans).

Final Thoughts

Some year might come along that is worse than 1968 for new retirees. Maybe 2022 will turn out to be a worse time to retiree since the late 60s. Perhaps in 30 years we’ll know that for 2022, the initial safe withdrawal rate was 4.2% instead of 4.4%.

But can we really predict that based on current conditions, when the 4% rule has survived much worse? I don’t think so.

Rob is a Contributing Editor for Forbes Advisor, host of the Financial Freedom Show, and the author of Retire Before Mom and Dad–The Simple Numbers Behind a Lifetime of

Source: Will Inflation And The Stock Market Conspire To Kill The 4% Rule?


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How To Turn Your Retirement Account Into a Personal Pension Plus

Just as you insure your home against the risk of fire and flood, so too can you insure another of your most valuable investments from risk: your retirement savings.

Retirement is a source of significant anxiety for Americans. It’s reported 40% of us fear retirement more than death. Outside of government jobs, pensions have nearly all disappeared. Important changes aimed at addressing some systemic issues are coming, but experts like Wade Pfau believe new Social Security legislation may not be enough. Combined with the potential of a recession (as the bull market keeps running), economic pressures posed by COVID-19, and 10,000 Baby Boomers retiring every day, this is hardly surprising.

With the near extinction of employer-provided pensions, Americans increasingly have to figure out their own retirement income plan, though many of us lack the tools or training to do so.

The ‘Fragile Decade’

Financial literacy is an often-neglected area of education among Americans; this causes financial planning to feel opaque and overwhelming. For many, retirement boils down to, “How much money do I need to save by the time I retire?” But it’s not that simple, and not planning for sequence-of-returns risk is a major pitfall.

Because retirement accounts are typically tied to the stock market, and the stock market is inherently volatile, it’s possible for an unexpected downturn to significantly impact a retiree’s income stream if it happens during the so-called “fragile decade” – the five years leading up to retirement and the five years that follow.

Simply put, if you experience significant losses due to some combination of withdrawals and poor performance during the fragile decade, it is difficult to recover. You’re in a position where your earning years are either behind you or almost behind you, and most of your retirement (if not all of it) is still ahead. Given that retirement can last 30 years or more, that could spell disaster during your most vulnerable years. That’s sequence-of-returns risk, or sequence risk.

Insuring Your Retirement Like You Insure Your Home

So, is your retirement at the mercy of the risks inherent in the stock market? Maybe. But it doesn’t have to be. An annuity can be an effective way to ensure your retirement’s durability by reducing your income stream’s exposure to market risks. Just as you insure your home against the risk of fire and flood, so too can you insure another of your most valuable investments from risk: your retirement savings.

Some financial advisers have been hesitant to offer their clients annuities, for a variety of reasons. Among these reasons are high costs and limited liquidity, as well as the lack of a death benefit. Many believe they’re just too complicated. While these complaints were true of some types of annuities, they aren’t true in general. Not anymore.

These objections are being overcome as modern annuities tend to be simpler and less costly. These innovations have inspired many financial advisers to change their position on annuities; in fact, a 2021 survey conducted by RetireOne and Protective Life found fewer than a quarter of financial advisers would not recommend an annuity to a client, even if it was the best fit for the client’s needs.

But some of those objections still are worth examining. Most annuities do have liquidity restrictions and many are not historically good at protecting against inflation.

Contingent Deferred Annuities

A contingent deferred annuity (CDA) has the same overall advantage of other income annuities – guaranteed income regardless of stock market downturns, badly-timed withdrawals, and so forth – but this type of annuity sidesteps some of the remaining hurdles.

A CDA acts as a sort of “risk wrapper” for your IRAs, Roth IRAs and taxable brokerage accounts, but the insurance portion is unbundled from the underlying accounts so that investments in ETFs and mutual funds may be covered. The amount of income you receive from the CDA (your coverage base) is calculated from the total of your initial investment, and will not drop below that amount, no matter what the markets do. In fact, your coverage base may go up, and those annual income payments can range from 3% to 6%. Keep in mind that excess withdrawals CAN impact your coverage base, however.

The CDA’s income payments trigger when you need them and are paid by the insurance company for the rest of your life, even after your assets are depleted. Until then, your financial adviser continues to manage your retirement assets for you.

This means that, if the stock market trends very well, the accounts the CDA is safeguarding will grow and so will the amount that your income payments are based on, giving you a bigger cushion later in life. But if the market does poorly and your accounts shrink, your CDA continues to pay out at the same rate, regardless of how poorly your investments perform. And, subject to the claims paying ability of the insurance company, they continue even if the underlying accounts are depleted. It’s guaranteed income for life.

How Do CDAs Work?

That sounds great, right? But you’re probably asking how it all works and, perhaps most importantly, what it’ll cost. Again, this is insurance. It isn’t free. But, it’s all more straightforward than you might think.

The first question to ask is: What do I want to cover? A CDA is typically designed to cover mutual funds and ETFs. The best CDAs offer many approved mutual funds and ETFs to choose from. The chances are your retirement accounts are already set up to work with them. You decide the total value you want to insure, and that sets your initial coverage base.

It’s important to reiterate that these funds stay where they are. Your financial planner continues to manage them, and you retain the same level of control you always had. In some cases, you can continue to add funds to that coverage base, too. Depending on the specific CDA you’re paying for, you may even increase the income you get from the CDA by doing so. You can also withdraw funds from your retirement account normally, though withdrawing funds too frequently can have an adverse impact on your annuity income.

Once you trigger your payments, those payments continue for life. They’re withdrawn from the covered accounts, but the rate of payment stays constant even if the value of the covered accounts drops – even if it drops to zero.

Another salient point: You don’t need to trigger payments if you don’t need that income, and you can cancel that coverage once you feel confident that your other retirement income streams are sufficient to maintain your quality of life. If you don’t want to pay fees for coverage you don’t need, then you don’t have to.

And speaking of those fees, you’re usually looking at something about 1% to 2.2% of the account value withdrawn each year from the accounts being covered. Those fees can be variable, based on the account value, or they can be fixed based on your total initial investment. A fixed fee means your fee is established when you establish your initial coverage base, and it remains constant as account values fluctuate. The fee does not increase if your retirement accounts give you particularly good returns, but the reverse is also true: If your accounts do poorly, you don’t see a reduction in your fees.

Here’s one of the best parts: Triggering your payments doesn’t necessarily trigger a taxable event. If you’ve been deferring your taxes with a Roth IRA, covering that Roth with a CDA allows you to draw income from that account upon retirement, without the usual tax implications of withdrawing money from a traditional IRA or a taxable account.

All these benefits make CDAs an efficient method for de-risking your portfolio as you near retirement. It’s a great way to make the fragile decade less fragile.

A ‘Personal Pension Plus’

Pensions are rare these days. Entire generations have entered the workforce without the promise of a pension. Your parents may have pensions. But do you have one? Probably not.

A CDA can turn your existing retirement accounts into something very pension-like, one that can protect your income during that crucial “fragile decade.” And, with the dual advantages of being able to cover retail mutual funds and ETFs, and the inheritability of the asset, a CDA really is a “Personal Pension Plus.”

When dealing with investment accounts, it is easy to get tunnel vision about Return on Investment, and how much money you have saved. But what you’re trying to achieve is the best quality of life possible, once your earning years are over. You want to have the greatest possible spending power during your retirement. A CDA can help you do that by turning your retirement account into a guaranteed income stream…for life.

Edward J. Mercier

Edward J. Mercier is president of RetireOne®. He has more than 25 years of experience spanning investment and insurance products, including sales, distribution, clearing and general management. He has held multiple senior leadership positions at Charles Schwab & Co., most recently as general manager of investment management distribution and clearing services.

Source: How to Turn Your Retirement Account Into a ‘Personal Pension Plus’


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How To Find a Buyer For Your Annuity

Remember to give a discount on the cash value of your payments. According to the industry group, the National Association of Settlement Purchasers, the maximum discount rate in the industry is 18%.

If you are looking for a buyer for an annuity, find out how to resell the value of your annuity. The number of payments you wish to sell, the amount of money you will receive, your payment plan (including the way payments are received), the current market situation, the RATING OF THE INSURANCE COMPANY THAT ISSUED the annuity, and any fees or other charges incurred on transferred annuities.

It is important to find a reputable bond buyer to guide you and explain the process. Sellers need to understand that they are not getting the full value of your pension until the company you are contracting out reviews the pension and makes an offer that is mutually beneficial. Once you have taken out your pension and agreed to the terms, you can mimic the transaction. 

In order to ensure careful consideration of pension scheme clauses, companies should ensure full transparency. They should offer personalized presentations outlining the non-guaranteed elements of the pension contract. It is recommended that you learn a few basic aspects before buying an annuity. =

If you sell an annuity in its entirety, YOU GIVE UP YOUR REMAINING INTEREST IN THE CONTRACT. You will receive the money left over from the payment of the contract, but no one else will receive future payments. If you buy an inherited annuity through a sales contract, you are the buyer, not the insurer. 

Another option is to sell the entire annuity, which can result in a much higher payout. Annuity holders may feel safer selling part of their pension than they do if they know they will get the payments on which they depend in the future. The time you sell the annuity passes and you get the remaining regular payments back.

Similar to partial sales, bondholders can sell part of their pension payments for a lump sum in lump sum sales. This means that they will receive a certain dollar amount that will be deducted from future pension structures for settlement payments. For example, you could sell years one to four of your pension in lump sums. 

Once you have decided how much money you need you can decide to sell the whole value of the annuity or part of it, either as a lump sum or as part of a certain NUMBER OF PAYMENTS. IF YOU DECIDE TO sell some or all of your payments, you continue to receive regular income and retain tax benefits. 

If you need cash immediately, you can sell the payments for a lump sum. You will receive a cheque for three payments at the time of sale and once the payments have passed through your annual pension, the cheque will be reinstated. If you sell part of your pension (or more) and need a cash lump sum in the future, you will need to repeat the process. 

For example, if you need $25,000 for a new car, you can sell the $25,000 of the value of your annual inventory. A company like DRB Capital buys part of your pension contract and gives you the money you need. You receive periodic payments for a certain number of years, but you can also receive and sell a lump sum if your annual payment amount is too low.

One of the biggest misconceptions about cashing in a pension is that future payments have to be sold. You have the right to cash in your pension if a third judge agrees. 

In other words, the sale and use of all annuities reduce the number of annuities you have. While selling an annuity can be a good option for reducing debt or settling financial hardship, this decision should not be taken lightly. There are ways to sell all annuities and it is important to check all of them to CHOOSE THE RIGHT ONE FOR YOUR NEEDS. In the same way, you will receive payments from a pension scheme on future dates.

An annuity can be bought as a lump sum in exchange for several future lump sums. If YOU CAN MEET YOUR CURRENT FINANCIAL NEEDS with money from your pension, you are ready to retire. Many pensioners keep the money they need and sell the rest of the value of their pension. They sell some of the value of the property and pay each other dividends on certain parts of the pension. Selling an annuity can be ONE OF THE BIGGEST FINANCIAL DECISIONS A PERSON CAN MAKE.

IN some cases, sellers opt for specialized financial firms such as the CBC Settlement Fund to handle their pension transactions, which can range from retirement accounts to trust funds. Some annuity buyers offer large lump sums to recipients of pensions who need to make regular payments on a lump sum basis. Large lump sums are usually less than the sum received by the beneficiary at the end of the term but the amount received at the end of the term is reduced by a so-called discount rate that gives the beneficiary MORE FLEXIBILITY TO MEET IMMEDIATE FINANCIAL OBLIGATIONS.

If you receive structured payments such as divorce settlements, child support payments, 401 (k) payouts, veterans benefits, or Social Security, you don’t have to sell your pension to raise money. Pension payments are subject to normal income tax when you receive them, but with guaranteed annuities for retirement, you only owe as much income tax on the money as on regular distributions. As we have already explained, there are many different types of pensions: annuities, lottery or jackpot pensions, deferred annuities, and more.

The first phase, known as the rewards payout phase, consists of a single series in which you receive a lump sum from the company. The lump-sum is the money with which you take care of financial obligations or changes in your life, such as STARTING YOUR OWN BUSINESS, BUYING A HOME, OR GOING to school.  It depends on the pension plan you are contracting out of, but generally speaking, paying a lump sum into one will set up the right accumulation period. 


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Can You Beat Inflation With A Monthly Annuity?

A century ago, money from Andrew Carnegie created Teachers Insurance & Annuity Association to pay pensions to schoolteachers, professors and other people who work at nonprofit organizations. In the early days, these pensions were backed by bond portfolios and paid fixed monthly sums. Then, in 1952, TIAA invented the variable annuity.

Payouts from this novel product were tied to the return on a collection of stocks called the College Retirement Equities Fund. Don’t put all your money in this risky thing, a retiring prof would be told, but put in some in order to keep up with the rising cost of living. Your payouts from Cref will be unpredictable but still very likely, over time, to greatly outpace payouts from a fixed annuity. That’s because stocks, over time, outpace bonds.

With the variable annuity, TIAA married the high returns on equities with the classic annuity benefit of longevity pooling. Longevity pooling means that people who die young collect less over their lifetimes than their colleagues who live long. Pooling is a bet worth making because it allows you do live well off a pot of savings without taking a risk that you will exhaust those savings. Pooling is how all monthly pensions work. It’s how Social Security works.

Cref was a hit. It now has $279 billion under management.

Is it a good buy? It looks that way to me. The graph displays the monthly payouts for a 67-year-old female who invested $100,000 25 years ago in the main stock account, which is akin to a global index fund with a 30% foreign allocation. She rode a roller-coaster, with payments cut in half during the crash of 2007-2009, but if she’s still breathing at 92 she’s now getting $2,146 a month, better than triple her $610 starting pension.

For the index fund, the combined fee (for salesmen, annuity administrators and portfolio managers) comes to 0.24% a year. In the world of annuities that counts as a bargain. Variable annuities sold by stockbrokers can cost eight times as much.

It helps that TIAA is a nonprofit and its annuity pools are run on a mutual basis—meaning, pensioners share in the gains and losses that arise from unexpected mortality. Thus, if too few emeritus professors take up skydiving, there will be more than the expected number of mouths to feed and the growth in payouts will be less than hoped for. Conversely, a pandemic boosts payouts.

Now, a mutual form of organization is no guarantee of either efficiency or wisdom, but in this context it means that the insurance company does not have to pad its prices in order to cover the risk that retirees will live too long.

Nor does the nonprofit status mean an advisor won’t be tempted to steer a pensioner into products considerably more costly than an index fund (read this New York Times story). But if you stick to the cheap portfolio options you’ve got a good deal. Proviso: You should be in excellent health if you’re buying any kind of annuity.

Alas, not everyone can get in the door at Cref. You can acquire a TIAA annuity only if you or a fairly close relative works or worked in the nonprofit world—such as for a government agency, hospital, school or college.

What variable annuity is there for retirees in the corporate sector? Nothing that I would recommend. The insurance industry has responded to TIAA’s invention with a slew of convoluted and costly products that make price comparisons next to impossible.

You will probably see some kind of “mortality” charge in the prospectus (that padding I was talking about); you will probably not be able to discern what kind of worse damage is built into the formula that connects your payout to the return on the stock market; your salesman will probably be buying a new sports car right after you sign.

If you are not eligible for TIAA, and if an advisor mentions variable annuities, flee. Find a better solution at Do-It-Yourself Income For Life.

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Do You Get Your Money’s Worth From Buying An Annuity?

Coin Stacks And Chart Graphs On A Chessboard

Once upon a time, in the (somewhat mythical) past of traditional defined benefit pensions, your employer protected you from the risk of outliving your money in retirement, by acting, more or less, as an insurance company providing an annuity. With that benefit receding into the past, many experts have been hoping that Americans with 401(k) plans would avail themselves of annuities on their own, to give themselves the same sort of protection, and, indeed, the SECURE Act of 2019 made it easier for those plans to offer their participants an annuity choice, and, when surveyed, 73% of those participants said they would “consider” an annuity at retirement.

At the same time, though, Americans distrust annuities — in part because traditional deferred annuities had high fees and expenses and only made sense in an era predating IRAs and 401(k)s, when they were attractive solely due to the limited tax-advantaged options for retirement savings. But that’s not the only reason — annuities, quite frankly, aren’t cheap.

How do you quantify the value of an annuity? In one respect, it’s subjective and personal: do you judge yourself to be in good health, or does family history and your list of medications say that you’ll be one of those with the early deaths that longer-lived annuity-purchasers are counting on? Do you want to be sure you can maintain your standard of living throughout your retirement, or do you figure that you won’t really care one way or another if you have to cut down expenses once you’re among the “old-old”?

But measuring the value of annuities, generally speaking, does tell us whether consumers are getting a fair deal from their purchases, and here, a recent working paper by two economists, James Poterba and Adam Solomon, “Discount Rates, Mortality Projections, and Money’s Worth Calculations for US Individual Annuities,” lends some insight.

Here’s some good news: using the costs of actual annuities available for consumers to purchase in June 2020, and comparing them to bond rates which were similar to the investment portfolios those insurance companies hold, the authors calculated “money’s worth ratios” that show that, for annuities purchased immediately at retirement, the value of the annuities was between 92% – 94% (give-or-take, depending on type) of its cost. That means that the value of the insurance protection is a comparatively modest 6 – 8% of the total investment.

But there’s a catch — or, rather, two of them.

In the first place, the authors calculate their ratios based on a standard mortality table for annuity purchasers — which makes sense if the goal is to judge the “fairness” of an annuity for the healthy retirees most likely to purchase one. But this doesn’t tell us whether an annuity is a smart purchase for someone who thinks of themselves as being in comparatively poorer health, or with a spottier family health history, and folks in these categories would benefit considerably from analysis that’s targeted at them, that evaluates, realistically, whether annuities are the right call and whether their prediction of their life expectancy is likely to be right or wrong.

In the second place, the 92% – 94% money’s worth calculation is based on the typical investment portfolio of insurance companies, approximated by the returns of BBB-rated bonds. This measures whether the annuity is “fair” or not, in that “moral” sense of whether the perception that the company is “cheating” is customers is real (it’s not).

But these interest rates are very low. The authors, in addition to their calculations of “money’s worth,” back into the implied discount rate from the annuity costs themselves. For men aged 65, that interest rate is 2.16%; for women aged 65, 2.18%.

Now, imagine that you compare this annuity to an alternative plan of investing your money in the stock market, earning 7% annual returns, and believing you can predict your death date (or not really caring if you fall short or end up with leftover money for heirs).

The cost of the protection offered by the annuity, the guarantee that you will never run out of money, and that you will not suffer from a market crash, is very expensive indeed — when you compare apples to oranges in this manner, the money’s worth ratio is, according to my very rough estimates, more like 60%, meaning that about 40% of your cash is spent to purchase the “insurance protection” of the annuity.

And, again, that’s not because insurance companies are cheating anyone; that’s solely because of the wide gap between corporate bond rates and expected returns when investing in the stock market— a gap which was particularly wide in the summer of 2020 when this study was competed, but remains nearly as wide now.

As it stands, Moody’s Baa rates are in the 3% range; in the 2000s, they were in the 6% range, and in the 1990s, from 7% – 9%. Although this drop in bond rates is good news for American homebuyers because this marches in tandem with mortgage rates, it makes it far harder for retirees to manage their finances in ways that protect them from the risks that they face in their retirement.

Perhaps interest rates in general, and bond rates specifically, will increase as we leave our current economic challenges, but there’s no certainty, and as long as this gap between bond rates and expected stock market returns remains so substantial, retirees will be challenged to find any sort of safe investment that makes sense for them. Which means that what seems like a great benefit for Americans looking to borrow money — for mortgages, car loans, credit cards — can pit the elderly against the young in a generational “us vs. them” contest.

As always, you’re invited to comment at JaneTheActuary.com!

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Yes, I’m a nerd, and an actuary to boot. Armed with an M.A. in medieval history and the F.S.A. actuarial credential, with 20 years of experience at a major benefits consulting firm, and having blogged as “Jane the Actuary” since 2013, I enjoy reading and writing about retirement issues, including retirement income adequacy, reform proposals and international comparisons.

Source: Do You Get Your Money’s Worth From Buying An Annuity?



An annuity is a series of payments made at equal intervals.[1] Examples of annuities are regular deposits to a savings account, monthly home mortgage payments, monthly insurance payments and pension payments. Annuities can be classified by the frequency of payment dates. The payments (deposits) may be made weekly, monthly, quarterly, yearly, or at any other regular interval of time. Annuities may be calculated by mathematical functions known as “annuity functions”.

An annuity which provides for payments for the remainder of a person’s lifetime is a life annuity.

Variability of payments

  • Fixed annuities – These are annuities with fixed payments. If provided by an insurance company, the company guarantees a fixed return on the initial investment. Fixed annuities are not regulated by the Securities and Exchange Commission.
  • Variable annuities – Registered products that are regulated by the SEC in the United States of America. They allow direct investment into various funds that are specially created for Variable annuities. Typically, the insurance company guarantees a certain death benefit or lifetime withdrawal benefits.
  • Equity-indexed annuities – Annuities with payments linked to an index. Typically, the minimum payment will be 0% and the maximum will be predetermined. The performance of an index determines whether the minimum, the maximum or something in between is credited to the customer.

See also


  • Kellison, Stephen G. (1970). The Theory of Interest. Homewood, Illinois: Richard D. Irwin, Inc. p. 45
  • Lasher, William (2008). Practical financial management. Mason, Ohio: Thomson South-Western. p. 230. ISBN 0-324-42262-8..
  1. Jordan, Bradford D.; Ross, Stephen David; Westerfield, Randolph (2000). Fundamentals of corporate finance. Boston: Irwin/McGraw-Hill. p. 175. ISBN 0-07-231289-0.
  • Samuel A. Broverman (2010). Mathematics of Investment and Credit, 5th Edition. ACTEX Academic Series. ACTEX Publications. ISBN 978-1-56698-767-7.
  • Stephen Kellison (2008). Theory of Interest, 3rd Edition. McGraw-Hill/Irwin. ISBN 978-0-07-338244-9.
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