In the US, annuities are big sellers among folks with lots of money, or folks who've just come into lots of money. The reason is primarily due to a tax code so complicated and unwieldy that it looks like a Rube Goldberg scheme, in that if you misjudge just one tiny step in the process, the monkey does not lean over and put the peanut in the hat at the end. Trying to figure out how to get that damn monkey to put the peanut in the hat are thousands of tax specialists throughout the country. Some of them are highly paid and some of them are just hanging on by the skin of their Form W-4Ps. Some of them are scrupulous and some of them would tell you your dying granny "whispered in my ear, just prior to passing" that she thought you should let HIM handle all of this "tax stuff" and not get stressed out, like you did when Timmy shot the schnauzer.

Basically, (don't you hate that word? Any time you hear someone speak or read something someone writes, and they start out a lot of their statements with, "Basically...", you should probably not pay much attention to anything else they say. If they throw in the hackneyed phrase, "the Bottom Line," this is a dead giveaway that they don't know Jack Shit about their topic.) Anyway, what was I saying? Oh yeah, basically the bottom line with annuities is that you hand money over to an insurance company (and no one can sell annuities except a licensed insurance company in the good ol' USA -- let's have a "God Bless America" from the peanut gallery on that one) and the insurance company will pay you a monthly income based on some formula for the rest of your life. The formula's bottom line is based on your life expectancy. (OK, I won't say that again. But remember that writers who throw in too many parenthetical remarks are also covering up for the fact that they are woefully inadequate to be discussing the issue at hand.)

In other words, let's say that you paid someone to kill your wealthy parents who have left you as their sole heir. Let's say that you get away with it. (I am not suggesting that anyone do this, of course. Unless they have really shitty parents with a lot of money.) Let's say that you come into a shit-load of cash and now you have a whole lot of "friends" you didn't have before. How are you going to handle this much money when you've never even done your own laundry, for Christ's sake? Well, one of your new friends might be a guy like me who will advise you to put that money into an annuity where you don't ever have to worry about a regular monthly income again, for your whole life (and he -- or, let's say "I" -- make a nice little commission). How much will that monthly income be? Well, if you're 30 and your life expectancy is 90 (which is actuarially not far off, if you've been lucky enough to reach the ripe old age of 30 without getting killed), that money has got to be structured to last 60 years. That's 720 months. So, in light of this, would a small monthly check when you could have all this cash at once seem like a logical option for a whorehopping crackhead such as yourself? Oh, well, you weren't the kind of client I was really looking for, anyway. I'd probably be investigated by the new "money laundering" team formed as a result of these motherhumping terrorists. When it was just drug money, no one really cared, but the government is getting serious about this stuff now. I tried to buy a new car with cash the other day and this prick . . . Oh, you don't want to hear about that, do you.

In the example above, if you did decide to hand over all of that money to me and let me begin a lifetime monthly income program for you, that would be called a Single Premium Immediate Annuity. This generally doesn't happen with younger folks because it doesn't have a lot of tax advantages. However, if you're a 65 year-old lady whose husband just died and left her a half a million dollars in a life insurance policy, that's enough monthly income at her life expectancy to make this a very viable option. Since the death benefit on a life insurance policy is tax-free (unlike the inheritance in the above example), the widow's only concern is the tax she'll face on the gain from the investment of this money. Leveling that income out over the rest of her life might sound pretty darn sensible to her.

A more common form of annuity is the Single Premium Deferred Annuity or Flexible Annuity. These both have tax ramifications which are attractive to some folks. In the Single Premium Deferred Annuity, the guy who had his parents offed in the above example would elect to give me all that inheritance money and not start paying it back to him until he was at least 59½ years old. Why that age? Because the interest earned on that money would not be counted as taxable income to him during all those years while he was salivating over the Annual Statements. He would have to pay taxes on the money at the time of withdrawal, but that's a whole lot of years of tax-deferred earnings prior to that time. At 59½ he could start making withdrawals without any penalty from the IRS except the normal income taxes due on the withdrawals. If he got greedy and wanted to get at some of that money prior to that age, there would be at least a 10% penalty on the money taken out, likely surrender charges from the insurance company, and the obligatory phone call from me saying, "What the fuck do you think you're doing, you idiot?" After all, I am his agent and I owe him my professional advice.

A Flexible Annuity is pretty much the same animal, except it involves scheduled payments into the account over a number of years as opposed to a lump sum investment. If anyone you know (or yourself) is contributing to an IRA, the chances are good that this is just a Flexible Annuity which is contributed to with what is called Qualified Money. The fancy word "Qualified" means that you get to take these contributions off of your taxable income each year, just like you would in a 401(K). That's a pretty big deal if you actually care about how much you pay in taxes. Anytime you can reduce your taxable income, that is saving you bucks aplenty, plus you're stashing away money "for that rainy day." In case you never knew what was meant by the phrase, "that rainy day," I can now reveal the secret to you. It means you're too damn old to work, or you're so cranky no one will hire you. Hopefully, it also means you're at least 59½ when this happens.

So what have we learned here? What's the bottom line, as they say? (Sorry.) First of all, your 401(K) is really just a Flexible Annuity to which you (and hopefully, your employer, too) are contributing. Many employers match some portion of your contributions to your 401(K) in a feeble attempt to apologize to you for no longer having a pension plan set up, like they did for your dad when he was working. You're probably on a "cash payout" pension of some sort, but the idea of getting a monthly check from your employer when you retire is likely a thing of the past. I don't know about your employer, but mine will match the first 6% of my income I put in my 401(K) dollar for dollar and match the next 6% at 50 cents on the dollar. That means for every $12 I contribute, the employer is putting in $9. And I get to take that $12 off my taxes when it comes time to feed the bloated beast called the Federal Government. All in all, this is a great deal you should all be taking advantage of it if you have the opportunity.

The second lesson you should take away from here is this: When you buy an annuity from me, I make money. So e/mail me if you need anything. I promise I "know nothing" about what happened to your parents. Wink, wink.

More abstractly, in general interest theory an annuity is any payment that is made regularly over a certain length of time. With the exception of the Arabic banking system that does not make use of interest, annuities are not particular to any economic system and are fairly widespread.

Examples of annuities are mortgage payments on a house, repayment of a loan in monthly installments and monthly payment of bills. In the first two cases the annuity has a predetermined end date, while in the third example the annuity has no apparent end date (You'll be paying bills for the rest of your life. Get used to it.) Special annuities with no end date are known as perpetuities. Another example of a perpetuity is the regular payments of health insurance, which only end with the death of the insured.

For annuities with a final date of payment, by the term of the annuity we mean the length of time for which the annuity is to be paid. The regular time intervals in which the payments of the annuity are made as known as the period of the annuity. The word "annuity" reminds us of a time when the periods were always years, but now the word has acquired a more broad meaning with other possible periods. For example, the payment of a loan might have a term of one year and period of one month if paid on monthly installments. If the payments are made at the end of the period, then we speak of an annuity-immediate, while annuities with payment at the beginning are annuities-due. The difference is small and not terribly important.

Because of the time value of money, (money you have today is more valuable than money you have tomorrow), the computation of the present value of an annuity can be a little interesting. If we take time value and interest rates into account, an annuity of twelve monthly payments of 1000 roubles is not worth 12,000 roubles today, but must be discounted in accordance with interest rates. An example should be make this clear.

Suppose that Vronsky and Karenin have made an agreement for Vronsky to repay a debt in the form of twelve monthly payments of 1000 roubles, and that the payments are made at the end of the month (an annuity-immediate), with the first payment on January 31st, 1878, and suppose that interest is compounded on the same day that payments are due. Suppose that Karenin is compassionate towards Vronsky's pride and wants to salvage him from the embarassment and discomfort of coming each month to his manor to pay the amount. Karenin being the the gentleman he is instead offers Vronsky the opportunity to repay the entire debt in one sum today, January 1st 1878, taking into account an interest rate of 8%.

In short, at an effective interest rate of 8%, how much is an annuity of twelve payments of 1000 worth today?

Because Karenin would prefer to have 1000 roubles today than by the end of January, we must discount the value of 1000 roubles at end of January by 108%, so they are in fact only worth 1000/1.08 = 925 roubles and 93 kopeks to Karenin today. With compound interest, the payment at the end of February is worth less, only 1000/(1.08)2 = 857 roubles and 34 kopeks, and that at the end of March is even less, a mere 1000/(1.08)3 = 793 roubles and 83 kopeks. And so on. A table may help:

Month    |  Payment due | Discount factor | Present value
January  |  1000        |  1/1.08         |   925.93
February |  1000        |  1/1.082        |   857.34
March    |  1000        |  1/1.083        |   793.83
April    |  1000        |  1/1.084        |   735.03
May      |  1000        |  1/1.085        |   680.58
June     |  1000        |  1/1.086        |   630.17
July     |  1000        |  1/1.087        |   583.49
August   |  1000        |  1/1.088        |   540.27
September|  1000        |  1/1.089        |   500.25
October  |  1000        |  1/1.0810       |   463.19
November |  1000        |  1/1.0811       |   428.88
December |  1000        |  1/1.0812       |   397.11

                                     TOTAL:  7536.07   

So because Karenin is considering such an attractive interest rate for Vronsky, Vronksy has the choice to pay only 7536 roubles and 7 kopeks today and save himself some embarassment in the face of Society.

The mathematically inclined will have no problems in recognising the geometric series involved with annuities and in devising appropriate general formulae, perpetuities being the case of infinite geometric series (convergence is assured if we assume positive interest rates). If an denotes the discounted value of one dollar at the end of n periods, i the rate of interest, and v = (1 + i)-1 the rate of discount, then

          1 - vn
     an = -------

Annuities-due require similar computations which can be simplified by the introduction of the concept of discount rate instead of interest rate. I leave these generalisations to the industrious reader.


Kellison, Stephen. The Theory of Interest McGraw-Hill, 1991.

An*nu"i*ty (#), n.; pl. Annuities (#). [LL. annuitas, fr. L. annus year: cf. F. annuit'e.]

A sum of money, payable yearly, to continue for a given number of years, for life, or forever; an annual allowance.


© Webster 1913.

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