# The Math of an indexed life annuity

Not long ago, I wrote an article on the math of annuities suggesting that you can’t really make the decision to buy a life annuity without some numbers.

The example I showed in that article was based on an example of Gerald who is 65 with \$100,000 in his RRSPs. A life annuity would pay him \$571.16 every month for the rest of his life.

In the comments, my blogging friend Micheal James wanted to know what indexing the income would do to the math. Let’s check out the analysis.

## Indexed life annuity

With an indexed life annuity, you have to select an annuity factor. I chose 2% (not that I know what the future inflation rate will be).

Here’s the results for a life annuity indexed at 2% for the same 65 year old male:

• Standard Life \$472.35
• Desjardin Financial Security \$471.76
• BMO Insurance \$457.51
• Manulife \$409.74

You can choose any inflation figure you want but the higher the inflation rate, the more the income is going to drop.

If we look at Standard Life, the \$472.35 is over 17% lower than the \$571.16. However, that income is going to go up by 2% per year every year and eventually it will catch up and surpass the \$571.16 that you could have gotten with the non-indexed annuity. That happens at age 75.

With the indexed annuity, although your income would catch up at age 75, you would still be behind in total income. you would have to wait until age 84 to just catch up with total income.

I don’t know about you but I would choose the non-indexed pension any day of the week with these numbers. Why wait till age 85 to get ahead with your income?

 non-Indexed annuity Indexed Annuity Male age 65 monthly annually cumulative monthly annually cumulative 65 \$571.16 \$6,853.92 \$6,853.92 \$472.35 \$5,668.20 \$5,668.20 66 \$571.16 \$6,853.92 \$13,707.84 \$481.80 \$5,781.56 \$11,449.76 67 \$571.16 \$6,853.92 \$20,561.76 \$491.43 \$5,897.20 \$17,346.96 68 \$571.16 \$6,853.92 \$27,415.68 \$501.26 \$6,015.14 \$23,362.10 69 \$571.16 \$6,853.92 \$34,269.60 \$511.29 \$6,135.44 \$29,497.54 70 \$571.16 \$6,853.92 \$41,123.52 \$521.51 \$6,258.15 \$35,755.69 71 \$571.16 \$6,853.92 \$47,977.44 \$531.94 \$6,383.31 \$42,139.01 72 \$571.16 \$6,853.92 \$54,831.36 \$542.58 \$6,510.98 \$48,649.99 73 \$571.16 \$6,853.92 \$61,685.28 \$553.43 \$6,641.20 \$55,291.18 74 \$571.16 \$6,853.92 \$68,539.20 \$564.50 \$6,774.02 \$62,065.21 75 \$571.16 \$6,853.92 \$75,393.12 \$575.79 \$6,909.50 \$68,974.71 76 \$571.16 \$6,853.92 \$82,247.04 \$587.31 \$7,047.69 \$76,022.41 77 \$571.16 \$6,853.92 \$89,100.96 \$599.05 \$7,188.65 \$83,211.06 78 \$571.16 \$6,853.92 \$95,954.88 \$611.04 \$7,332.42 \$90,543.48 79 \$571.16 \$6,853.92 \$102,808.80 \$623.26 \$7,479.07 \$98,022.55 80 \$571.16 \$6,853.92 \$109,662.72 \$635.72 \$7,628.65 \$105,651.20 81 \$571.16 \$6,853.92 \$116,516.64 \$648.44 \$7,781.22 \$113,432.42 82 \$571.16 \$6,853.92 \$123,370.56 \$661.40 \$7,936.85 \$121,369.27 83 \$571.16 \$6,853.92 \$130,224.48 \$674.63 \$8,095.59 \$129,464.85 84 \$571.16 \$6,853.92 \$137,078.40 \$688.12 \$8,257.50 \$137,722.35 85 \$571.16 \$6,853.92 \$143,932.32 \$701.89 \$8,422.65 \$146,145.00 86 \$571.16 \$6,853.92 \$150,786.24 \$715.92 \$8,591.10 \$154,736.10 87 \$571.16 \$6,853.92 \$157,640.16 \$730.24 \$8,762.92 \$163,499.02 88 \$571.16 \$6,853.92 \$164,494.08 \$744.85 \$8,938.18 \$172,437.20 89 \$571.16 \$6,853.92 \$171,348.00 \$759.75 \$9,116.94 \$181,554.14 90 \$571.16 \$6,853.92 \$178,201.92 \$774.94 \$9,299.28 \$190,853.43 91 \$571.16 \$6,853.92 \$185,055.84 \$790.44 \$9,485.27 \$200,338.70 92 \$571.16 \$6,853.92 \$191,909.76 \$806.25 \$9,674.97 \$210,013.67 93 \$571.16 \$6,853.92 \$198,763.68 \$822.37 \$9,868.47 \$219,882.14 94 \$571.16 \$6,853.92 \$205,617.60 \$838.82 \$10,065.84 \$229,947.99 95 \$571.16 \$6,853.92 \$212,471.52 \$855.60 \$10,267.16 \$240,215.15 96 \$571.16 \$6,853.92 \$219,325.44 \$872.71 \$10,472.50 \$250,687.65 97 \$571.16 \$6,853.92 \$226,179.36 \$890.16 \$10,681.95 \$261,369.60 98 \$571.16 \$6,853.92 \$233,033.28 \$907.97 \$10,895.59 \$272,265.19 99 \$571.16 \$6,853.92 \$239,887.20 \$926.13 \$11,113.50 \$283,378.70 100 \$571.16 \$6,853.92 \$246,741.12 \$944.65 \$11,335.77 \$294,714.47

Given this example, which annuity would you buy?

View Results

## Indexed pensions are very valuable

There is a strong lesson in this example. For those of you who are still part of a defined benefit pension plan that is indexed or even partially indexed, be very happy with the type of pension you have. For those of us without indexed defined benefit pensions, the math in this example suggests that indexing is too hard to replicate. Rarely would we choose the indexed annuity over the non-indexed annuity.

## Think twice before taking the commuted value

Over the past 10 years, I have met people who have changed employers before the age of 55 and they moved their defined benefit pension out to a Locked in Retirement Account (LIRA) assuming they could invest it and do better. Most of these people did not do better and worse yet, no one showed them the consequence of losing an indexed pension.

1. Michael James

It’s safer to get rising payments, but this is probably a harder sell for insurance agents because of the lower initial payments. I understand that Standard Life offers a CPI-indexed annuity, but it seems that the public can’t get quotes from them directly.

• Jim Yih

I’m not sure this is about what is being sold. If you were the consumer would you choose the indexed option here over the non-indexed option? If so, why?

I agree with the desire to get rising payments but only if the math or the numbers justify it. As you know, I don’t sell annuities or other financial products but this education is important before anyone buys and annuity.

Anyone else want to chime in?

2. wendi1

For me, an annuity would be longevity insurance (and a bit of declining ability insurance, as well – I can manage my investments now, but maybe not so much at 80).

If its purpose is to provide for you if you live longer than expected, the indexed one is the way to go (and I would really, really rather have one indexed to CPI).

I was surprised at the low payments, though – at 4%, without touching capital at all, I can get more than \$330 a month.

3. Scott F

@Michael James, I’m not sure what you mean by it being safer. As was pointed out, it would take about 19½ years to catch up in total income using an indexed @ 2% annuity. If someone invested the difference between the two payouts and got 3%, it would increase that date another 2 years (to 86½).

Given those numbers, I would prefer the non-indexed over the index. From the numbers I’ve seen, increasing to a 3% index drops the monthly payment another 10% from 2%. I would imagine a CPI indexed one would see an even greater drop due to the uncertainty.

@wendi1
Where are you going to find a guaranteed 4% these days though. Even if you could, having the same \$571.16 monthly to spend would mean you would run out just before you turned 87 years old.

4. Michael James

@Scott F: One of the dangers for those who buy annuities is having the value of payments inflated away. If you confidently spend your early payments, you may regret not saving some of them if future payments are worth much less due to a period of high inflation. Indexed payments will take longer to lose their value to high inflation. Even safer is a CPI-indexed annuity. Of course you pay for this added safety with lower initial payments.

5. Scott F

It’s not a perfect comparison, but when I calculated DI payment increases, the premium increase with one insurer for a 4% increase is the same as for a CPI based increase. Using that as a proxy, the monthly payment for a CPI indexed annuity is 68% of a non-indexed one.

In this example, that would be a payment starting at \$388.39. You would need CPI=4% to get the same monthly payment/total payments equality as above (75/84 years). 4% is high compared to where it’s been the past couple decades, but it’s not unrealistic (personally, when I run scenarios I use 3.5%)

6. Jay

Inflation is a real concern longer term (due to government printing money).

How about real return bonds? I’d love to see an article about how to make your own CPI indexed annuity buy buyoing a binch of those. And also if it’s comparable in value.

7. Anthony Holden

What should I tell the cashier when I buy my next lotto ticket, cash or annuity? Would it be best to take a lump sum payment or take it over a long term for a lotto player that is in his 30s?

8. Lewis H.

Nice article. Insurance companies and their agents rarely publish what annuities cost. You have to telephone them and wait until they get back to you. Never a self-serve website for getting instant quotes. With banks, it’s very easy to see what the current interest rate is on the latest GIC. It would help if we knew the date of these annuity numbers as with declining interest rates over time, the cost of these products is rising. Also, as the annuity purchase cost is higher for a woman due to higher life expectancy, it would be nice to at least propose an estimate of what percent higher for a woman.

9. TR

Does anyone actually sell an annuity that raises along with the CPI or do you just have to guess what number inflation might be when buying an inflation adjusted annuity? I am looking to buy an annuity similar to the CPP that tracks the CPI. Thanks

• Arnold T

I have the same question as TR. Is it possible to get an annuity that is indexed to CPI?

10. kevin

I’m thinking about purchasing an annuity in 2017 with about 1/4 of my savings.I like the idea I don’t have to worry about investments and I have always been jealous of defined pension plans. I have a small one , but not enough. I like Wendy’s point while we may be able to manage our financial portfolios now, what about when we are eighty. And whose to say that we make a couple of horrid financial bets between now and then?

11. dipak

how to invest your LIRA, if you r not yet 65 yrs.