Definition of annuity

Question

To my understanding, an annuity is a contract you make with, let's say, an insurance company. You pay the principal and they commit to pay you regularly a certain for a period of time, which might be until your death.

My problems come with the regular payments and the goal of an annuity. I am very new to finance so take my questions with a grain of salt.

Are the regular payments supposed to give you back the principal (and maybe an interest) when the annuities stop? Contrary to a bond, it is not clear to me if you are supposed to get all your money back at the end. I have only seen that you get regular payments. If they are huge yes, if they are small why pay for the contract?

From what I understand naively, either it is

1. a service you pay for them to keep the money and make you payments later, when you might need it, so you are guaranteed to lose some money,
2. an investment you make, which is supposed to give your money back at the end, the risk being that the insurance company fails before it happens,
3. an investment you make, but depending on the income you will get, you might lose or win money at the end.

Is one of the three somewhat close to reality?

What is the discount rate, or the interest rate that is used for the computation of the present value of an annuity (see here for example)? Does it have anything to do with the regular payment?

Answer 1

It's essentially 3. But it's also a risk-transfer exercise.

A common type of annuity is a pension for life. You save money in a pension fund while you are working. So when you retire, you have a big lump sum of money that you hope will last you for the rest of your life. But you don't know how long you're going to live, and you don't know how well your pension fund will do for the next 10 to 30 years.

You could leave the money invested, and take a monthly drawdown. Take too little and the fund keeps growing while you live in poverty. Take too much and the money runs out before you die.

Alternatively, hand over the whole pension pot to an insurance company and buy an annuity. In return, they guarantee you a pension for the rest of your life. If you die next year, they keep your money. If you live until you are 100, then they have to keep paying.

Answer 2

In brief, with an annuity you are purchasing a guaranteed income stream at a constant rate even if you outlive the initial principal and the returns upon it. The insurance company, looking at their actuarial tables, is betting that you do not outlive the money and/or that they can make enough profit investing it to more than pay for the payments they make to you, either of which represents profit to them.

I purchased an annuity with about 5% of my retirement investments, to give myself a higher guaranteed income stream then Social Security. (And perhaps a better guaranteed one, if certain politicians ever have their way, though I honestly believe their threats are mostly fear tactic campaigning father than reality.) But it's a small amount because it is just a safety net and reassurance; I believe I will do better by simply keeping my money invested until I need it.

Answer 3

Imagine if planting a $20 bill sprouted a money tree, which yields $1 every year, forever. Then $20 today is worth the same as $1 every year, forever. The fraction of its cost a tree yields annually is the discount rate i.

In real life, money doesn't grow on trees, and building a money factory has been known to attract federal agents. Annuity is a legal way to make this trade.

An annuity has no principal. The money you've invested no longer exists for you; all you have now is a tree, which you can harvest annually.

There are different kinds of annuities:

• A perpetuity never expires, yielding that i forever;
• A regular annuity is a money tree that lives N years;
• A life annuity is a money tree that dies with you.

The discount rate, in all cases, is the average return of a theoretical zero-risk investment. Annuities with a limited lifespan are expected to pay more the discount rate.

A life annuity is a bet on your lifespan - you're betting you'll live longer than N, the company less, where N is how many years a competing fixed term annuity with the same yield would last. Should you live forever, the company has sold you a perpetuity for the price of an annuity.

To give examples, the fair present value of a $10,000/year annuity at a 5% discount rate is:

• $200,000 for a perpetuity
• $124,622 for a 20-year annuity
• $77,217 for a 10-year annuity

Thus, if a company sells you a life annuity of $10,000 for $125,000, they're staking $75,000 (their maximum loss if you do live forever), with an over/under at 20 years, to win up to $125,000 if you depart before the first payment. You're betting $125,000 that you'll live for more than 20 years from now, winning $10,000 for each year that you do.

Answer 4

Annuities are also insurance for insurance companies. If you sell life insurance and people start dying earlier (e.g. due to Covid), then you have a problem. But if you are also selling annuities, then the extra money you have to pay out for life insurance will be offset by the money you’re saving on annuity payments.