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The math of life annuities

The math of life annuities
The math of life annuities
Written by Jim Yih
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 CompanyMonthly incomeEmpire Life$571.16Desjardin Financial$570.33BMO Insurance$557.00Standard Life$556.15Manulife$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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