# The math of life annuities

Recently, Rob Carrick released a video on The lowdown on annuities in his Let’s Talk Investing Series.  Although the information in the video was good, it was missing one very important piece when it comes to determining if annuities are right for you.  It was missing NUMBERS.

Life Annuities are one area where theory is not enough to make decisions.  What we know is annuities are great because they provide GUARANTEED, LIFETIME income.  The problem is they are inflexible and have no potential for higher returns.  Let’s add some math to the mix to help you determine if an annuity is right for you.

## Gerald is 65

Gerald has \$100,000 in his RRSPs and he is ready to take some income to supplement his retirement.  The first step for Gerald is to get an annuity quote.  Here’s what he got from an insurance agent:

 Insurance Company Monthly income Empire Life \$571.16 Desjardin Financial \$570.33 BMO Insurance \$557.00 Standard Life \$556.15 Manulife \$502.14

The first lesson with annuities is shop around.  As you can see, there is a big difference between the best and the worst and we are talking about lifetime income here.

## Is this a good deal or not?

If we take \$571.16 and multiply it by 12, we get an annual income of \$6,853.92 per year.  If we divide that number into the \$100,000, that translates to a 6.85% yield on the capital.

Although 6.85% sounds good when GICs are paying less than 3%, don’t be mislead by this number.  Unlike a GIC, if you pass away, you do not get the \$100,000 back.  Part of the \$571.16 payment is interest and the other portion is repayment of capital.  The only way to get your \$100,000 back is to live long enough.

## How long do you have to live?

It’s not perfect math but if you take a simple approach and divide \$571.16 into \$100,000, you get 175 months to get back your \$100,000 with no interest.  That’s 14 and a half years.  That put’s Gerald at 79 and a half.

In other words, Gerald could take his \$100,000 and put it in a savings account that paid no interest an pull out \$571.16 every month until he ran out of money at age 79 and a half.  How do you like that math?

If we assumed the saving account earned 2%, that would extend the longevity of the \$100,000 to just over 18 years or age 83.  At 3% return, the \$100,000 would last to age 85.

If you can tell me when Gerald is going to die, I can tell you which is the better deal?  If you know for sure that Gerald is going to live past 85, then the math suggests that the annuity will pay off over a GIC.

## What about mutual funds or things that could earn higher potential returns?

If you invested in something that potentially earned higher returns like mutual funds or Exchange Traded Funds (ETFs), you might be able to make the \$100,000 last longer.  At 5% returns, the \$100,000 would last over 26 years and Gerald would be in his 90’s.  However, we’ve seen periods, even longer ones where non-guaranteed investments have not earned 5%.

The other problem with non-guaranteed investments like mutual funds and stocks is the withdrawal math on variable returns can really work against you.  Check out an article I wrote on the Balance Junkie site to see the risk of withdrawing money in a variable return environment

In the end, my point is simple:  You can’t determine if annuities are right for you unless you run the numbers.  This math was very specific for a 65 year old Male. Changing the age and gender will change the results so you cannot use this math to make general conclusions about life annuities.

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### Written by Jim Yih

Jim Yih is a Fee Only Advisor, Best Selling Author, and Financial Speaker on wealth, retirement and personal finance. Currently, Jim specializes in putting Financial Education programs into the workplace.For more information you can follow him on Twitter @JimYih or visit his other websites Group Benefits Online and Advisor Think Box.

### 14 Responses to The math of life annuities

1. Michael callahan says:

Great post! Good to see some real life numbers.

2. I’m with you that you have to look at numbers to make big decisions like this. It seems to me that it would be much safer to have a CPI-indexed annuity. That \$571 per month could shrink up after a few years of 5% or higher inflation. There seem to be many U.S. options for this, but I’m told that there is only one in Canada.

3. Thanks for running us through the math Jim. I love concrete examples like this!

4. peter gosselin says:

Great article,
I am 72,was thinking about an annuity,are the numbers any better.

5. The book “Your Retirement Income Blueprint” has some great ideas to take advantage of annuities in an efficient way. It notes that a lot of people buy annuities in their 70s and even 80s. In addition to asking if you’ll live to 83, you should ask if you want to buy an annuity when you’re 83!

Insurance companies very reasonably pay a much higher return at that point. In some cases it might make sense to use shorter-term capital preserving options at first and then buy an annuity later. If the numbers work out (of course) you could end up with more capital when you’re younger and more security when you’re older.

6. Great post, Jim! Putting down numbers really helps.

I agree with Value Indexer. It’d be great to see the numbers for someone buying an annuity at 75 or older. I understand they make more sense at that age because the “mortality credits” become larger and boost the monthly returns considerably.

• Larry/Jim,

http://www.milliondollarjourney.com/how-annuities-work.htm

The key is to have permanent life insurance many years before retirement. Term is great if you like renting or plan to die before 65 but the real story is most people die after age 65. Also, unlike term you can not get all your money back plus interest.

Since many have been raised on the buy term and invest the difference model we know that really does not work.

Insurance (which what annuities is) lowers your risk.

cheers,

Brian

• Hoshmand says:

you can’t touch it until the annuity date, even then depneding on the contract structure you probably will get payments, not the whole thing. You can check with a bank to see if you are able to collaterally assign the annuity against a loan, but since it is profit sharing, it is probably owned by your previous employer, so they would have to sign the assignment forms. good luck

7. Sorry, I just tried to vote your post a 5-star rating but clicked on the wrong button and brought the average down. If you can, please change it to the top rating.

8. Bona Savone says:

This assumes he has no spouse to continue the payments if he was to die first.It also assumes he has no guarantees on his annuity which I would never recommend buying an annuity without guarantees so that the remaining payments or commuted value could be paid to the beneficiaries.This way he doesn’t lose any capital if he dies sooner!

9. Scott F says:

When were those numbers quoted? Based on numbers I ran today, monthly payments are about \$70-\$80 higher, the highest is \$655. Granted, that was taken from a web site and may be a teaser rate but that shaves 21 months off your 175 month payback. So, it looks like market timing plays a role in buying an annuity as well.

The highest rate for a 75 year old male is \$923. That would be a 109 month pay back (age 84 1/12).

If one really wants to leave an inheritance an insured annuity strategy may make sense as well.

• Scott,

The problem(s) with annuity quote you get from the internet is one they are all ready out date.

Two there is no taxable amount quoted.

Example:

A 70 year old male (non -registered) may get \$8,100 per year guaranteed for life and only pay \$222 a year in taxes!

Interest rates are low however, taxes are still high and after taxes one needs to find a 6% GIC.

The quotes (annuity) cost the insurance agent \$20 each to get a number of different insurance companies to compare to.

So when one looks at the Toronto Star (web site) for example, the annuity quotes are very limited and no taxable amounts are quoted.