Calculating Annuity Payments

Calculating Annuity Payments

Introduction

This article explains calculating annuity payments for a given annuity value and structure.

What is an Annuity?

An annuity is quite simply a series of payments over time. Different types of annuities define those payments, the number of them, their amount, and their timing, in different ways.

Calculating Annuity Payments – Simplest Example

Suppose you want to define an annuity that is worth $100 today. The simplest case would be to define an annuity with 1 payment, of a known amount, upfront. What would the amount of that payment be?

Well it would obviously be $100. If we paid out more than $100 – it would be worth more than $100. If we paid out less, it would be worth less. So to calculate the annuity payments for an annuity worth $100 with 1 known payment upfront, then it would be clearly a single payment of $100.

Calculating Annuity Payments – Adding Complexity

Suppose for the number of payments, we’re going to flip a coin. So there’s a 50/50 chance of there being either 1 payment or 2 payments. And suppose the payments come back to back basically upfront, 1 day after another. And we want that annuity to still be worth $100. How do we calculate the annuity payments that get there?

Well if we made both the payments $100 – 50% of the time we’d pay out $100 and 50% of the time we’d pay out $200. So on average we’d be paying out $150. If we calculate the annuity payments like that, then our annuity value wouldn’t be the $100 we want. So we have to lower the payments.

What if we still flip a coin and reduce the payments to $50 each. Then 50% of the time we’d pay out $50, and the other 50%, $100. So on average we’d be paying out $75. That’s too low. So for our annuity to be worth more $100, with this uncertain number of payments (1 or 2), we need to pay out more than $50 for each payment.

What if the payments were $70? Then 50% $70, 50% 140 – so on average $105. Now we’re getting close to $100!

So calculating annuity payments for this annuity – with an uncertain number of payments that will be 1 or 2 years, with a flat known payment, we know if we want it to be worth $100 today we need the payment to be a bit less than $70!

Lessons From Calculating Annuity Payments – Complexity

We can solve for that exact amount too. While it’s not really complicated, it’s clearly more complicated than the first example. Note when we added a little complexity, there’s still a clear solution for calculating annuity payments, it just makes it a bit more challenging to do.

So what does this have to do with calculating annuity payments for my annuity?

Your annuity has some value. Maybe you gave an insurance company $100,000 and asked them to pay it back to you as an annuity. Or maybe a balance collected in a pension and it’s being paid out to you over time.

It has a structure for the number of payments – maybe they’re known, like our first example, or maybe they’re not (e.g. they continue until you die, or they continue until both you and your spouse die, or maybe they payout for at least 10 years no matter want, and then if you’re still alive they continue until you die)

In calculating those annuity payments, what insurance companies and actuaries do – is exactly what we did above. They look at the amount of the payments, and the number of payments, and the timing of payments. And they value those precisely – to come up with what the value of the annuity would be, calculating annuity payments with all the assumptions.

If you give an insurance company $100,000 and they agree to define an annuity for you – they define some profit they want to make for their work. Suppose they want to make $25,000 on the transaction. Then they calculate annuity payments, so their value today, amidst uncertainty, is ~ $75,000. They promise to pay you those payments, which they know on average will be worth $75,000 today and they make the difference in profit.

The key principal here, is the more complex an annuity is to compute,the tougher an tougher it is for a consumer to understand. And the net result is it allows for greater and greater profit margins for the insurance company.

If you have an annuity, and your looking at the calculated annuity payments, and trying to understand them, it’s important to ask an actuary to help you.

The annuity payments are a game just like a casino game. And just like at the casino, different games (payout structures) lay you different odds.

How do I use this?

I offer independent actuarial services to value your unique annuity for you, with complete details – so you can better understand what you have, and evaluate the choices available to you.  It is very difficult to find an actuary focused on helping consumers better understand their insurance products (instead of helping insurance companies sell them).  I am one!

You can hire me for help understanding your annuity and calculating annuity payments here: Hire me To Help Calculating Annuity Payments and Valuing Annuity Choices

Resource from Society of Actuaries on Calculating Annuity Payments